Knewton Alta - Chapter 2 - Descriptive Statistics Part 2
Based on the box-and-whisker plot you constructed above, which area of the plot has potential outliers?
Distance between the minimum and Q1 The length of the lower whisker line is long compared to the upper whiskers. The lower values may contain outliers.
Quartiles
The values that divide the data into four equal parts
The sample minimum and sample maximum
are the two values that show the range of the data set. The sample minimum is the least value in the ordered data set. The sample maximum is the greatest value in the ordered data set.
The following data set provides Oklahoma data on benchmark jobs and relationship to market. The next department you look at is Information Systems. What is the median salary for those employees?
median=50606.16 The 2nd quartile or 50th percentile is the same as the median. The median is the 167th employee, which makes $50,606.16.
outliers
values that are very different from the rest of the values in a data set
Elliot likes to find garden snakes in his backyard and record their lengths. Estimate the mean of the lengths (in inches) of the garden snakes given in the following grouped frequency table. Round the final answer to one decimal place.
11.5 Remember that to estimate the mean, we first find the midpoint of each interval: MidpointFrequency5.579.5613.51217.55 Now, we treat this as if it were a regular frequency table. We take each midpoint multiplied by its frequency, add them up, and divide by the total number of values. The sum is 5.5⋅7+9.5⋅6+13.5⋅12+17.5⋅5=345 We find the total number of values by adding up the frequency column: 7+6+12+5=30 Finally, dividing the sum by the total number of values, we find our mean estimate of the lengths (in inches) of the garden snakes is: Mean estimate=34530=11.5
The following data set provides wage information of Seattle by subdivisions. Background: You are interviewing for the job of Compensation Specialist for the city of Seattle. The hiring manager shows you the database for wage and classification information from February 2017. She asks you: What are the job titles of the two persons with the highest hourly rates in the second quartile of the Arts and Culture Department?
Administrative Staff Assistant and Stage Tech,Lead When separating the jobs into the quartiles, you see that the two job titles with the highest hourly rates in the second quartile of the Arts and Culture Department are Administrative Staff Assistant and Stage Tech,Lead.
The following frequency table of data represents the costs of perfumes at a department store, what is the potential outlier?
Correct answer: 29 Note that most of the values are between 16 and 23, whereas 29 is far above the rest of the values. Therefore, 29 is the potential outlier. Since this data represents costs of perfumes at a certain department store, the outlier shows an uncommon occurrence. Managers may choose to sell the outlier perfume at a lower price.
Find the median of the following list of dollars spent per customer at a cheese shop in the last hour. 32,19,21,16,27,15
It helps to put the numbers in order. 15,16,19,21,27,32 Now, because the list has length 6, which is even, we know the median number will be the average of the middle two numbers, 19 and 21. So the median number of dollars spent per customer at a cheese shop in the last hour is 20
five-number summary
is descriptive statistics that provides information about the five most important percentiles from the data set
mode
the number(s) that occurs most often in a data set
The following data set provides New York City school based programs cost by borough The five number summary of cost for school based programs in the Manhattan borough is given here. Minimum $35,263, Q1 $63,617, Median $507,206.5, Q3 $1,324,622, Maximum $4,667,715. Using the interquartile range, which of the following are outliers? Select all correct answers.
4,667,715 IQR=Q3−Q1 IQR=1,324,622−63,617=$1,261,005 To find any lower outliers:Q1−1.5(IQR)=63,617−1.5(1,261,005)=507,206.5−1,891,507.5=$−1,827,890.5There are no numbers below this level. To find any upper outliers:Q3+1.5(IQR)=1,324,622+1.5(1,261,005)=1,324,622+1,891,507.5=$3,216,129.5There is only one number more than $3,216,129.5, so there is only one outlier, $4,667,715.
Given the following list of the number of pens randomly selected students purchased in the last semester, find the median. 13,7,8,37,32,19,17,32,12,26
Correct answers:$\text{median=}18\text{ pens}$median=18 pens It helps to put the numbers in order. 7,8,12,13,17,19,26,32,32,37 Now, because the list has length 10, which is even, we know the median number will be the average of the middle two numbers, 17 and 19. So the median number of pens randomly selected students purchased in the last semester is 18.
Find the mode of the following amounts of exercise (in hours) randomly selected runners completed during a weekend. 2,14,14,4,2,4,1,14,4,4,8
Note that 4 occurs 4 times, which is the greatest frequency, so 4 is the mode of the amount of exercise (in hours) randomly selected runners completed during a weekend.
Find the mode of the following number of times each machine in a car factory needed to be fixed within the last year. 2,5,6,12,14,12,6,2,5,3,14,5
Note that 5 occurs 3 times, which is the greatest frequency, so 5 is the mode of the number of times a machine in a car factory needed to be fixed within the last year
The following frequency table summarizes a set of data. What is the five-number summary?
1. In a frequency table, the value column represents the number and the frequency column represents how many times that number appears. So we can write that the number 2 happens 3 times. So now we can write the data from least to greatest: 2,2,2,3,3,3,4,5,7,8,8,8,8,10,10,10,11,12,12 2. and 3. We can immediately see that the minimum value is 2 and the maximum value is 12. 4. If we add up the frequencies in the table, we see that there are 19 total values in the data set. Therefore, the median value is the one where there are 9 values below it and 9 values above it. By adding up frequencies, we see that this happens at the value 8, so that is the median.5. Now, looking at the lower half of the data, there are 9 values there, and so the median value of that half of the data is 3. This is the first quartile. 6. Similarly, the third quartile is the median of the upper half of the data, which is 10. 2,2,2,3,3,3,4,5,7,8,8,8,8,10,10,10,11,12,12 So the five-number summary is MinQ1MedianQ3Max2381012
The following frequency table summarizes 60 data values. What is the 80th percentile of the data?
17 Use k=80 and n=60 to calculate i. i=80100(60+1)=48.8 Since this is not an integer, round 48.8 up to 49 and down to 48. The 48th value in the ordered set is 17 and the 49th value is 17. The average of 17 and 17 is 17. So, the 80th percentile is 17.
The five number summary for a set of data is given below. Min Q1 Median Q3 Max 50 51 80 83 87 What is the interquartile range of the set of data?Enter just the number as your answer. For example, if you found that the interquartile range was 18, you would enter 18.
32 Remember that the interquartile range is the third quartile minus the first quartile. So we find that the interquartile range is 83−51=32 This summary could represent bidding items bought on Ebay. A manager of those products could see the IQR is large and decide to choose permanent prices to reduce a wide range on sold items.
The dataset below represents the population density per square mile of land area in 25 states in the 2010 U.S. Census. What is the 17th percentile? 1,19,35,43,49,55,56,56,63,67,94,105,110,168,175,181,212,231,239,351,461,595,738,839,9857
46 Use k=17 and n=25, to calculate i. i=17100(25+1)=4.42 Since this is not an integer, round 4.42 up to 5 and down to 4. The 4th value in the ordered set is 43, and the 5th value in the set is 49. The average of 43 and 49 is 46. So, the 17th percentile is 46.
Which interquartile range (IQR) is much smaller than the other three regions?
East The East region has a very tight spread of tuition costs, so its IQR is the smallest.
Estimate the mean of the amounts (in dollars) randomly selected customers spent on chocolate chip cookies at a winter fair given in the following grouped frequency table. Round the final answer to one decimal place.
Remember that to estimate the mean, we first find the midpoint of each interval: Now, we treat this as if it were a regular frequency table. We take each midpoint multiplied by its frequency, add them up, and divide by the total number of values. The sum is 1.5⋅5+5.5⋅6+9.5⋅13+13.5⋅1=177.5 We find the total number of values by adding up the frequency column: 5+6+13+1=25 Finally, dividing the sum by the total number of values, we find our mean estimate of the amounts (in dollars) randomly selected customers spent on chocolate chip cookies at a winter fair is: Mean estimate=177.525=7.1
The following table shows 44 data values, sorted and arranged in rows of 5. What is the 3rd quartile of the data? 1 4 6 7 7 9 12 13 13 14 14 14 14 15 17 26 27 29 30 36 43 47 47 48 49 51 55 55 59 63 65 70 70 70 78 83 89 92 93 96 96 99 99 99
quartile=70 Remember that the 3rd quartile is the value which has 75% of the values below it. Because there are 44 values in the set of data, we compute (44)⋅(75%)=33. So we want the value P which has 33 values less than or equal to P.Looking through the table, we find that there are 33 values less than or equal to 70, so the 3rd quartile is 70. A hotel uses percentiles to see how their beds compare to several other hotels. For example (using the same data), a rating scale of 1−100 was taken from 44 hotels. Hotel A has a rating of 65 and from this data, we know that is below the 3rd quartile since the 3rd quartile is 70.
The following data set provides wage information of Seattle by subdivisions. Arrange the Departments in ascending order of the maximum hourly rate.
Arts and Culture, City Auditor, City Budget The maximum hourly rate for the three departments in ascending order is: Arts and Culture ($62.59), City Auditor ($72.84), and City Budget ($86.83).
The five number summary for a set of data given below represents completed projects in a certain department. MinQ1MedianQ3Max 50 62 84 96 99 Using the interquartile range, which of the following are outliers? Select all correct answers.
Correct answer: 3 4 6 Remember that outliers are numbers that are less than 1.5⋅IQR below the first quartile or more than 1.5⋅IQR above the third quartile, where IQR stands for the interquartile range.The interquartile range is the third quartile minus the first quartile. So we find IQR=96−62=34 So a value is an outlier if it is less thanQ1−1.5⋅IQR=62−(1.5)(34)=11or greater thanQ3+1.5⋅IQR=96+(1.5)(34)=147So we see that 3, 4, and 6 are outliers. Since this summary represents completed projects in a department, the manager could see that the outliers are due to new employees or allow changes for even dispersement.
The five number summary for a set of data is given below. MinQ1MedianQ3Max 69 74 81 85 87 What is the interquartile range of the set of data?Enter just the number as your answer. For example, if you found that the interquartile range was 24, you would enter 24.
Correct answers:$11$11 Remember that the interquartile range is the third quartile minus the first quartile. So we find that the interquartile range is 85−74=11
Find the median of the numbers in the following list. 10,7,15,6,24,20,1
It helps to put the numbers in order. 1,6,7,10,15,20,24 Now, because the list has length 7, which is odd, we know the median number will be the middle number. In other words, we can count to item 4 in the list, which is 10. So the median is 10.
Given the following frequency table of values, is the mean or the median likely to be a better measure of the center of the data set?
Median Most of the values are close together in the range between 40 and 45, but because there is one number, 70, which is much larger than the rest of the values, the mean would not be a good measure because that one large value would pull the mean up. Therefore, the median is probably a better measure of the center of this data set.
A hotel owner is deciding whether to buy new parts, hire a plumber, or allow no changes due to possible issues with the water pressure. To help make her decision, the data set lists the number of complaints about the water pressure at the hotel. For this data set, the minimum is 3, the median is 15, the third quartile is 16, the interquartile range is 4, and the maximum is 19. Construct a box-and-whisker plot that shows the number of complaints. Move the median first, then the first and third quartiles, and last the minimum and maximum.
Remember that the interquartile range is the third quartile minus the first quartile. Since we know the third quartile is 16, and the interquartile range is 4, we find that the first quartile must be 16−4=12. Since the box-and-whisker plot represents the five number summary of a set of data, the left end of the left whisker is the minimum value (3), the left edge of the box is the first quartile (12), the line in the middle of the box is the median (15), the right edge of the box is the third quartile (16), and the right end of the right whisker is the maximum value (19).
Put the interquartile ranges in order from smallest to largest.
The IQR is represented by each regions block of color. This appears easy to sort. The smallest IQR is East, then South, West, and Midwest with the largest IQR.
A manager at a shoe factory would like to find the mean number of breaks taken by employees on a particular Friday. He collects data from 15 fellow coworkers in the factory. The graph shows the frequency for the number of breaks taken during this time period. Find the mean number of breaks for the 15 coworkers, and round your answer to the nearest tenth. Record your answer by dragging the purple point to the mean.
The frequency graph shows the frequency for each data value. So, we can compute the mean by added up all the data values and dividing by the total number of data values. 3⋅1+5⋅2+3⋅3+2⋅4+1⋅5+0⋅6+1⋅7/15=42/15=2.8. Rounding to the nearest tenth, we have the mean is 2.8.
The following data set provides wage information of Seattle by subdivisions. Select all the statements that are true:
The lowest hourly rate in the Arts and Culture Department is the same as the lowest hourly rate in the City Budget Department. The first quartile hourly rates in the City Auditor Department are within the pay range of the fourth quartile hourly rates in the Arts and Culture Department. The higest pay in the second quartile of the City Auditor employee hourly rate are within a dollar of the lowest pay in the third quartile. Three statements are true: A. The lowest hourly rate in the Arts and Culture Department is the same as the lowest hourly rate in the City Budget Department. Both are $16.12. C. The first quartile hourly rates in the City Auditor Department ($43.86 to $52.10) are within the pay range of the fourth quartile hourly rates in the Arts and Culture Department ($40.45 to $62.59). E. The highest pay in the second quartile of the City Auditor employee hourly rate ($56.07) is within a dollar of the lowest pay in the third quartile ($56.24). Two statements are false: B. The lowest hourly rate in the Arts and Culture Department ($16.12) is not the same as the lowest hourly rate in the City Auditor Department ($43.86). D. The number of people in the second quartile in the City Auditor Department is not different than the number of people in the third quartile of that department. Both quartiles have wage information on two people.
The following data set provides wage information of Seattle by subdivisions. What is the lowest hourly rate in the fourth quartile of the Arts and Culture Department?
$40.93 The lowest hourly rate in the fourth quartile of the Arts and Culture Department is $40.93.
Find the five-number summary of the following data set. 1,2,4,5,6,8,8,10,19
1. First, order the data from least to greatest: 1,2,4,5,6,8,8,10,19 2. The sample minimum is the least value, which is 1. 3. The sample maximum is the least value, which is 19. 4. The median (second quartile) is the middle number in the ordered set. Since this data set has an odd number of values, the middle number is in the set. The median is 6. 5. The first quartile can be found in the lower half of the data set: 1,2,4,5 There are two 'middle numbers' in the lower half of the set, so you need to take the average of 2 and 4. (2+4)2=62=3, so the first quartile is 3. 6. The third quartile can be found in the upper half of the data set: 8,8,10,19 There are two 'middle numbers' in the upper half of the set, so you need to take the average of 8 and 10. (8+10)2=182=9, so the third quartile is 9.
The following frequency table summarizes 60 data values. What is the 3rd quartile of the data?
18 Remember that the 3rd quartile is the value which has 75% of the values below it. Because there are 60 values in the set of data, we compute (60)(75%)=45. So we want the value P which has 45 values less than or equal to P.Looking through the table, we find that there are 45 values less than or equal to 18, so the 3rd quartile is 18.
The five number summary for a set of data given below represents the cost of ads between different magazines owned by the same company. MinQ1MedianQ3Max 57 64 66 76 80 Using the interquartile range, which of the following are outliers? Select all correct answers.
Correct answer: 36 96 117 Remember that outliers are numbers that are less than 1.5⋅IQR below the first quartile or more than 1.5⋅IQR above the third quartile, where IQR stands for the interquartile range.The interquartile range is the third quartile minus the first quartile. So we find IQR=76−64=12 So a value is an outlier if it is less thanQ1−1.5⋅IQR=64−(1.5)(12)=46or greater thanQ3+1.5⋅IQR=76+(1.5)(12)=94So we see that 36, 96, and 117 are outliers. Since this data represents the cost of ads in magazines all owned by the same company those in charge could steer those with a larger ad budget to the top outliers and those with a lower ad budget to the bottom outliers.
Which areas of the plot for the Midwest and West regions have potential outliers?
Correct answer: Distance between the minimum and Q1 The length of the lower whisker line for both the Midwest and the West is long compared to the upper whiskers. The lower values may contain outliers.
The following data set provides Oklahoma data on benchmark jobs and relationship to market. You make some final calculations about the Information Systems (IS) staff. Which of the following statements are true? Select all that apply.
Correct answer: IS staff at the 25th percentile earn a salary of $44,237.21. IS staff at the 75th percentile earn a salary of $56,109.65. The IS staff at the median salary earn more than the CAD specialists at the 45th percentile. The calculations of the percentiles and quartiles confirm the correct answers. The only one that is not correct is D. The 87th percentile of the HR staff earn less than the IS staff at the 75th percentile. The numbers are $53,350.12 versus $56,109.65.
In the census population density data set, what are the first, second and third quartiles? 1,19,35,43,49,55,56,56,63,67,94,105,110,168,175,181,212,231,239,351,461,595,738,839,9857
Correct answer: Q1: 55.5 Q2: 110 Q3: 295 First, find the median (or second quartile). There is an odd number of data points, and so the median is the middle number, 110. To find the first quartile, you need to find the middle number (median) of the lower half of the data. There is an even number of data points, so the first quartile is the average of the two middle data points, 55 and 56. The first quartile is 55.5.To find the third quartile, you need to find the middle number (median) of the upper half of the data. There is an even number of data points, so the third quartile is the average of the two middle data points, 239 and 351. The third quartile is 295.
John is the owner of a flower shop in New York City.The changes in weather and temperature are key factors for his inventory. The data below are the monthly average high temperatures for New York City. What is the five-number summary? 40,40,48,61,72,78,84,84,76,65,54,42
Correct answer: Sample minimum: 40, Sample maximum: 84 Q1: 45, Median: 63, Q3: 77 The five-number summary must be found using a data set that is ordered from least to greatest. Once ordered, the sample minimum is the smallest value, and the sample maximum is the largest value. The median is the middle value, which separates the data set into a lower half and an upper half. Q1 is the median of the lower half of the data set, and Q3 is the median of the upper half of the data set.
The following table shows 56 data values, sorted and arranged in rows of 5. What is the 2nd quartile of the data? 1 2 5 7 7 9 10 11 11 14 15 15 15 18 18 18 22 22 22 23 26 27 28 33 34 34 35 38 38 39 41 42 45 48 52 52 54 58 59 61 65 66 68 70 79 84 87 87 87 88 89 91 93 96 97 98
Correct answer: quartile=38 Remember that the 2nd quartile is the value which has 50% of the values below it. Because there are 56 values in the set of data, we compute (56)⋅(50%)=28. So we want the value P which has 28 values less than or equal to P.Looking through the table, we find that there are 28 values less than or equal to 38, so the 2nd quartile is 38. A hospital uses percentiles to see how their emergency room compares to several other hospitals. For example (using the same data), a rating scale of 1−100 was taken from 56 hospitals. Hospital A has a rating of 22 and from this data, we know that is below the 2nd quartile since the 2nd quartile is 38.
The dataset below represents the population density per square mile of land area in 15 states in the 2010 U.S. Census. What is the interquartile range 1,19,35,43,49,55,63,94,105,110,175,231,239,351,738
Correct answers:$188 Find the median, which is 94. Q1 and Q3 can be calculated by finding the medians of the lower and the upper half of the data set, separated by the median. Q1 is 43, and Q3 is 231. The interquartile range is the difference between Q3 and Q1. 231−43=188, so the interquartile range is 188.
The following data set provides Oklahoma data on benchmark jobs and relationship to market. You find the spread in salaries for HR staff is much larger than that for the CAD (Computer Aided Drafting and Design) specialists. You calculate the 33rd percentile of HR staff salaries to find how it compares to your previous calculation. What is that salary?
Correct answers:$37,175.56 There are 236 HR employees, so the 33rd percentile is between the 78th and the 79th employee. Both of them make the same salary, $37,175.56.
What is the potential outlier in the population density data set? 1,19,35,43,49,55,63,94,105,110,175,231,239,351,738
Correct answers:$738 But to be sure a value is an outlier, check if the data value is less than Q1−1.5 (IQR), or greater than Q3+1.5 (IQR). Q1−1.5(IQR)=43−1.5(188)=43−282=−239 Q3+1.5(IQR)=231+1.5(188)=231+282=513 The value 738 is greater than 513 so it is an outlier.
Find the median of the following set of data. 7,26,7,9,11,4,15,22
Correct answers:$\text{median=}10$median=10 It helps to put the numbers in order. 4,7,7,9,11,15,22,26 Now, because the list has length 8, which is even, we know the median number will be the average of the middle two numbers, 9 and 11. So the median is 10.
The following data set provides wage information of Seattle by subdivisions. In how many different quartiles would you find people with the job classification of Strategic Advisor 2, Exempt, in the City Budget Department?
Correct answers:3 The City Budget Department has people with the job classification of Strategic Advisor 2, Exempt, in all quartiles of the compensation spreadsheet except for the the first quartile.
Find the mode of the following amounts (in thousands of dollars) in checking accounts of randomly selected people aged 20-25. 2,4,4,7,2,9,9,2,4,4,11
If we count the number of times each value appears in the list, we get the following frequency table: Note that 4 occurs 4 times, which is the greatest frequency, so 4 is the mode of the amounts (in thousands of dollars) in checking accounts of randomly selected people aged 20-25.
Given the following list of values, is the mean or the median likely to be a better measure of the center of the data set?29, 56, 27, 29, 27, 28, 28, 30, 30, 27
Median Most of the values are close together in the range between 27 and 30, but because there is one number, 56, which is much larger than the rest of the values, the mean would not be a good measure because that one large value would pull the mean up. Therefore, the median is probably a better measure of the center of this data set.
Find the mode of the following number of states randomly selected travelers at a service plaza visited in the past three years. 18,13,8,8,13,10,13,10,9,18
Note that 13 occurs 3 times, which is the greatest frequency, so 13 is the mode of the number of states randomly selected travelers at a service plaza visited in the past three years.
The following frequency table summarizes a set of data. What is the five-number summary?
MinQ1MedianQ3Max 2 4 8 10 12 We can immediately see that the minimum value is 2 and the maximum value is 12.If we add up the frequencies in the table, we see that there are 19 total values in the data set. Therefore, the median value is the one where there are 9 values below it and 9 values above it. By adding up frequencies, we see that this happens at the value 8, so that is the median. Now, looking at the lower half of the data, there are 9 values there, and so the median value of that half of the data is 4. This is the first quartile. Similarly, the third quartile is the median of the upper half of the data, which is 10.2, 2, 3, 3, 4, 4, 5, 7, 7, 8, 8, 8, 8, 10, 10, 10, 11, 12, 12So the five-number summary is MinQ1MedianQ3Max 2 4 8 10 12 Plant Director can use a five-number summary to see the layout of number of projects completed per manager. The lowest number of projects completed was 2, the most 12 with a median score of 8. The median of the lower half 4, and upper half 10. This could tell the plant director if projects should be distributed differently among managers.
The following frequency table summarizes a set of data. What is the five-number summary?
MinQ1MedianQ3Max 5 6 11 13 16 We can immediately see that the minimum value is 5 and the maximum value is 16.If we add up the frequencies in the table, we see that there are 15 total values in the data set. Therefore, the median value is the one where there are 7 values below it and 7 values above it. By adding up frequencies, we see that this happens at the value 11, so that is the median.Now, looking at the lower half of the data, there are 7 values there, and so the median value of that half of the data is 6. This is the first quartile. Similarly, the third quartile is the median of the upper half of the data, which is 13.5, 5, 5, 6, 6, 7, 9, 11, 11, 11, 13, 13, 13, 15, 16So the five-number summary is MinQ1MedianQ3Max 5 6 11 13 16
The following frequency table summarizes a set of data. What is the five-number summary?
MinQ1MedianQ3Max 7 8 11 14 17 We can immediately see that the minimum value is 7 and the maximum value is 17.If we add up the frequencies in the table, we see that there are 15 total values in the data set. Therefore, the median value is the one where there are 7 values below it and 7 values above it. By adding up frequencies, we see that this happens at the value 11, so that is the median.Now, looking at the lower half of the data, there are 7 values there, and so the median value of that half of the data is 8. This is the first quartile. Similarly, the third quartile is the median of the upper half of the data, which is 14.7, 7, 8, 8, 8, 10, 10, 11, 13, 13, 14, 14, 16, 17, 17So the five-number summary is MinQ1MedianQ3Max 7 8 11 14 17 A new T-Shirt shop can use a five-number summary to see the layout of number of sweaters sold per day. The lowest number of sweaters sold was 7, the most 17 with a median score of 11. The median of the lower half 8, and upper half 14. This could tell the shop if they should keep selling sweaters or look at another item.
The following frequency table summarizes a set of data. What is the five-number summary?
MinQ1MedianQ3Max 7 9 13 15 17 We can immediately see that the minimum value is 7 and the maximum value is 17.If we add up the frequencies in the table, we see that there are 15 total values in the data set. Therefore, the median value is the one where there are 7 values below it and 7 values above it. By adding up frequencies, we see that this happens at the value 13, so that is the median.Now, looking at the lower half of the data, there are 7 values there, and so the median value of that half of the data is 9. This is the first quartile. Similarly, the third quartile is the median of the upper half of the data, which is 15.7, 8, 9, 9, 9, 10, 13, 13, 13, 15, 15, 15, 16, 16, 17So the five-number summary is MinQ1MedianQ3Max79131517
Given the following list of data, What is the five-number summary?2, 5, 7, 7, 9, 9, 9, 10, 10, 11, 12
MinQ1MedianQ3Max2791012 We can immediately see that the minimum value is 2 and the maximum value is 12.There are 11 values in the list, so the median value is the one where there are 5 values below it and 5 values above it. We see that this happens at the value 9, so that is the median.Now, looking at the lower half of the data, there are 5 values there, and so the median value of that half of the data is 7. This is the first quartile. Similarly, the third quartile is the median of the upper half of the data, which is 10.So the five-number summary is MinQ1MedianQ3Max2791012 A restaurant can use a five-number summary to see the layout of customer satisfaction scores about their service. For this, a scale of least 1 - most 12 could have been used with 1 not being selected. The lowest satisfaction score used was 2, the most 12 with a median score of 9. The median of the lower half 7, and upper half 10. This could tell the restaurant whether to train employees more or keep with their standards.
Given the following frequency table of values, is the mean or the median likely to be a better measure of the center of the data set
Most of the values are close together in the range between 33 and 37, but because there is one number, 20, which is much smaller than the rest of the values, the median is probably a better measure of the center of this data set.
Given the following list of values, is the mean or the median likely to be a better measure of the center of the data set?39, 41, 38, 39, 38, 41, 41, 39, 40
Most of the values are close together in the range between 38 and 41. There are no very large or very small values in the list, so the mean is a good measure of the center because it takes into account all the values but will not be pulled up or down by any one value.
The following data set provides New York City school based programs cost by borough. Carol examines a five number summary. She is given four numbers which are options to be outliers. If the numbers are above the maximum, or below the minimum, are they automatically identified as outliers?
No If a number is outside of the five number maximum and minimum, it does not necessarily mean it is an outlier. The IQR can help to determine potential outliers. An outlier is a data point that is significantly different (or far away) from the other data values. Outliers may be errors or some kind of abnormality, or they may be a key to understanding the data.
The following data set provides New York City school based programs cost by borough. The five number summary of cost for school based programs in the Brooklyn borough is given here. Minimum $35,263, Q1 $150,000, Median $738,703.5, Q3 $1,711,568, Maximum $5,704,790. Using the interquartile range, which of the following are outliers? Select all correct answers.
No outliers IQR=Q3−Q1 IQR=1,711,568−150,000=$1,561,568 To find any lower outliers:Q1−1.5(IQR)=150,000−1.5(1,561,568)=150,000−2,342,352=$−2,192,352There are no numbers less than $−2,192,352. To find any upper outliers:Q3+1.5(IQR)=1,711,568+1.5(1,561,568)=1,711,568+2,342,352=$4,053,920There are no numbers above this level. So, there are no outliers listed.
The frequency table below summarizes a list of the amounts (in dollars) randomly selected customers spent on hot chocolate during a winter festival. Find the mean. v-f 8-5 9-2 10-5 11-2 12-2 13-2 14-2 15-3
Remember that the mean is the sum of all the numbers divided by the number of numbers. The frequency table tells you the number of time that each number appears in the set of data. So to get the sum of all the numbers in the set of data, we take each frequency multiplied by its value and add them all up: Sum=8⋅5+9⋅2+10⋅5+11⋅2+12⋅2+13⋅2+14⋅2+15⋅3=40+18+50+22+24+26+28+45=253 The number of numbers in the list is the sum of the frequencies. Number of numbers=5+2+5+2+2+2+2+3=23 So the mean of the amounts (in dollars) randomly selected customers spent on hot chocolate during a winter festival is SumNumber of numbers=25323=11
Given the frequency table below for a list of recorded lengths (in inches) of randomly sampled garden snakes, find the mean. V-F 9-8 10-3 11-2 12-2 13-1 14-1 15-3
Remember that the mean is the sum of all the numbers divided by the number of numbers. The frequency table tells you the number of time that each number appears in the set of data. So to get the sum of all the numbers in the set of data, we take each frequency multiplied by its value and add them all up: Sum=9⋅8+10⋅3+11⋅2+12⋅2+13⋅1+14⋅1+15⋅3=72+30+22+24+13+14+45=220 The number of numbers in the list is the sum of the frequencies. Number of numbers=8+3+2+2+1+1+3=20 So the mean of the recorded lengths (in inches) of randomly sampled garden snakes is SumNumber of numbers=22020=11
Jon loves to go bird watching at a nearby animal sanctuary. Find the mean of the following numbers of birds he spotted at the sanctuary in the last few days. 14,10,17,11,9,15,6,14
Remember that the mean is the sum of the numbers divided by the number of numbers. There are 8 numbers in the list. So we find that the mean number of birds spotted is 14+10+17+11+9+15+6+14////8 = 96 96/8 = 12
The following data set provides New York City school based programs cost by borough.
The five number summary of cost for school based programs in the Bronx borough is given here. Minimum $35,239, Q1 $116,987, Median $194,696, Q3 $827,996, Maximum $12,035,084. What is the interquartile range of the set of data?Enter just the number as your answer. For example, if you found that the interquartile range is 25, you would enter 25.
The following data set provides New York City school based programs cost by borough.
The five number summary of cost for school based programs in the Manhattan borough is given here. Minimum $35,263, Q1 $63,617, Median $507,206.5, Q3 $1,324,622, Maximum $4,667,715. Using the interquartile range, which of the following are outliers? Select all correct answers.
A student would like to find the mean number of people living in households in a neighborhood. She collects data from 65 homes in the area. The graph shows the frequency for the number of people living in the homes. Find the mean number of people living in the 65 homes, and round your answer to the nearest tenth. Record your answer by dragging the purple point to the mean.
The frequency graph shows the frequency for each data value. So, we can compute the mean by added up all the data values and dividing by the total number of data values. 3⋅1+6⋅2+7⋅3+8⋅4+12⋅5+14⋅6+15⋅7/65=317/65≈4.88. Rounding to the nearest tenth, we have the mean is 4.9.
A music teacher would like to find the mean number of songs people listen to on the way home from work. She collects data from 18 teachers at the school. The graph shows the frequency for the number of songs the teachers listen to on their way home from work. Find the mean number of songs listened to for the 18 teachers, and round your answer to the nearest tenth. Record your answer by dragging the purple point to the mean.
The frequency graph shows the frequency for each data value. So, we can compute the mean by adding up all the data values and dividing by the total number of data values. 0⋅1+1⋅2+2⋅3+2⋅4+3⋅5+2⋅6+8⋅71///8=99/18=5.5. Rounding to the nearest tenth, we have the mean is 5.5.
The following data set provides wage information of Seattle by subdivisions. The range of salaries is greater in the Arts and Culture Department than in the City Auditor Department. True or False
True Salaries in the Arts and Culture Department go from from $16.12 to $62.59, a range of $46.47. Salaries in the City Auditor Department go from $43.86 to $72.84, a range of $28.98.
median
a number that splits a data set in half, with one half smaller and one half larger; the center or middle value of a data set
For example (using the same data), a rating scale of 1−100 was taken from 40 companies. A company uses percentiles to see how their profits in their market are compared to several other companies. The following table shows 40 data values taken from those 40 companies, sorted and arranged in rows of 5. What is the 70th percentile of the data? 1 5 6 7 8 17 18 18 22 29 31 39 43 46 50 50 51 55 55 57 59 62 64 67 71 72 75 77 77 82 85 92 92 92 93 93 95 98 98 100
percentile=77 Remember that the 70th percentile is the value which has 70% of the values below it. Because there are 40 values in the set of data, we compute (40)⋅(70%)=28. So we want the value P which has 28 values less than or equal to P.Looking through the table, we find that there are 28 values less than or equal to 77, so the 70th percentile is 77. A company uses percentiles to see how their profits in their market are compared to several other companies. For example (using the same data), a rating scale of 1−100 was taken from 40 companies. Company A has a rating of 82 and from this data, we know that is above the 70th percentile since the 70th percentile is 77.
mean
the sum of all the items in a list divided by the number of items in the listThe term Mean is often used interchangeably with the term Average