Stat 200 exam 2

Réussis tes devoirs et examens dès maintenant avec Quizwiz!

Use the Empirical Rule. The mean speed of a sample of vehicles along a stretch of highway is 63 miles per​ hour, with a standard deviation of 4 miles per hour. Estimate the percent of vehicles whose speeds are between 51 miles per hour and 75 miles per hour.​ (Assume the data set has a​ bell-shaped distribution.) Approximately ________% of vehicles travel between 51 miles per hour and 75 miles per hour.

97%

After constructing a relative frequency distribution summarizing IQ scores of college​ students, what should be the sum of the relative​ frequencies?

If percentages are​ used, the sum should be​ 100%. If proportions are​ used, the sum should be 1.

Why should the number of classes in a frequency distribution be between 5 and​ 20?

If the number of classes in a frequency distribution is not between 5 and​ 20, it may be difficult to detect any patterns.

Explain how to find the range of a data set. What is an advantage of using the range as a measure of​ variation? What is a​ disadvantage? Explain how to find the range of a data set. Choose the correct answer below.

The range is found by subtracting the minimum data entry from the maximum data entry. -------------------- What is an advantage of using the range as a measure of​ variation? It is easy to compute. ------------------------ disadvantage? It uses only two entries from the data set.

The ages of the winners of a cycling tournament are approximately​ bell-shaped. The mean age is 28.3 ​years, with a standard deviation of 3.4 years. The winner in one recent year was 32 years old. ​(a) Transform the age to a​ z-score. ​(b) Interpret the results. ​(c) Determine whether the age is unusual.

z = (value-mean)/SD= 1.09 1.09 above the mean No comma this value is not unusual. A​ z-score between minus 2 and 2 is not unusual.

Heights of men on a baseball team have a​ bell-shaped distribution with a mean of 175 cm and a standard deviation of 7 cm. Using the empirical​ rule, what is the approximate percentage of the men between the following​ values? a. 154 cm and 196 cm b. 168 cm and 182 cm a.) _________​% of the men are between 154 cm and 196 cm. b.) __________% of the men are between 168 cm and 182 cm.

a.) 99.7% b.)68%

The​ weights, in​ pounds, of packages on a delivery truck are shown in the​ stem-and-leaf plot. Find the​ mean, the​ median, and the mode of the​ data, if possible. If any measure cannot be found or does not represent the center of the​ data, explain why.

mean: 30 center of data ------------------ median:32.5 center of data ----------------- mode: 22,35 not represent a typical data set

​(a) Find the​ five-number summary, and​ (b) draw a​ box-and-whisker plot of the data. 4 8 8 5 1 9 8 7 9 5 9 4 1 6 2 9 8 7 7 9 min: q1: q2: q3: max:

min: 1 q1:4.5 q2:7 q3: 8.25 max: 9

Determine whether the statement is true or false. If it is​ false, rewrite it as a true statement. The second quartile is the median of an ordered data set.

true

A​ student's score on an actuarial exam is in the 78th percentile. What can you conclude about the​ student's exam​ score?

The student scored higher than​ 78% of the students who took the actuarial exam.

Determine whether the approximate shape of the distribution in the histogram shown is​ symmetric, uniform, skewed​ left, skewed​ right, or none of these. Justify your answer.

The shape of the distribution is skewed right because the bars have a tail to the right.

Determine whether the approximate shape of the distribution in the histogram shown is​ symmetric, uniform, skewed​ left, skewed​ right, or none of these. Justify your answer.

The shape of the distribution is uniform because the bars are approximately the same height.

The data set below represents the ages of 36 executives. Find the percentile that corresponds to an age of 64 years old. 28 29 34 34 34 39 39 41 42 44 46 46 46 46 47 48 49 50 50 52 53 54 56 56 59 60 61 61 62 62 62 63 64 64 64 65

# before 64/ total #

The depths​ (in inches) at which 10 artifacts are found are listed. Complete parts​ (a) and​ (b) below. 24.1 39.8 30.8 31.2 46.6 28.2 30.9 27.1 30.2 34.8

22.5 -------------------- Change 46.6 to 65.3 and find the range of the new data set. 41.2

Use the frequency polygon to identify the class with the​ greatest, and the class with the​ least, frequency.

29.3-32.5 What are the boundaries of the class with the least​ frequency? 11.5-14.5

What are some benefits of representing data sets using frequency​ distributions? What are some benefits of using graphs of frequency​ distributions? What are some benefits of representing data sets using frequency​ distributions?

Organizing the data into a frequency distribution can make patterns within the data more evident.

Use the given frequency distribution to find the ​(a) class width. ​(b) class midpoints. ​(c) class boundaries.

class width: 36-32 = 4 ------------------------------------ Midpoint: ((lower class limit) + (upper class limit)) / 2 32-35: (32+35)/2 = 33.5 36-39: (36 + 39)/2 = 37.5 40-43: 41.5 44-47: 45.5 48-51: 49.5 52-55: 53.5 56-59: 57.5 --------------------------------------- Class boundries: Lower class limit − 0.5 Upper class limit + 0.5 32-35: 31-.5, 35+.5 = 31.5, 35.5 36-39: 35.5, 39.5 40-43: 39.5, 43.5 44-47: 43.5, 47.5 48-51: 47.5, 51.5 52-55: 51.5, 55.5 56-59: 55.5, 59.5

​(a) Find the​ five-number summary, and​ (b) draw a​ box-and-whisker plot of the data. 4 8 8 5 2 9 8 7 9 6 9 4 2 6 2 9 8 7 7 9

min: 2 q1: 4.5 q2:7 q3:8.5 max:9

​(a) Find the​ five-number summary, and​ (b) draw a​ box-and-whisker plot of the data. 3 8 8 6 2 9 8 7 9 6 9 3 1 6 2 9 8 7 7 9

min= 1 q1 = (n+1 / 4)th value of the observation = 4.5 q2=7 q3=8.5 max= 9

The midpoints​ A, B, and C are marked on the histogram. Match them to the indicated scores. Which​ scores, if​ any, would be considered​ unusual?

point A: -1.42 B: 0 c = 2.13 unusual= 2.13

The data set below represents the ages of 36 executives. Find the percentile that corresponds to an age of 34 years old.

17

Determine whether the following statement is true or false. If it is​ false, rewrite it as a true statement. The mean is the measure of central tendency most likely to be affected by an outlier.

true

Determine whether the approximate shape of the distribution in the histogram shown is​ symmetric, uniform, skewed​ left, skewed​ right, or none of these. Justify your answer.

The shape of the distribution is skewed left because the bars have a tail to the left.

Why is the standard deviation used more frequently than the​ variance?

The units of variance are squared. Its units are meaningless.

How is a Pareto chart different from a standard vertical bar​ graph?

The bars are positioned in order of decreasing height with the tallest bar on the left.

The depths​ (in inches) at which 10 artifacts are found are listed. 31.4 35.5 33.2 34.1 44.7 29.1 23.8 32.8 23.9 24.7 The range of the given data set is 20.9. If the current​ maximum, 44.7​, is replaced with 51.1​, the range then becomes 27.3. Compare these values and determine how outliers affect the range of a data set. How does changing the maximum value affect the​ range?

The range is greatly affected by this change.

What is the difference between a frequency polygon and an​ ogive?

A frequency polygon displays class frequencies while an ogive displays cumulative frequencies.

Determine whether the statement is true or false. If it is​ false, rewrite it as a true statement. In a frequency​ distribution, the class width is the distance between the lower and upper limits of a class.

False. In a frequency​ distribution, the class width is the distance between the lower or upper limits of consecutive classes.

Describe the relationship between quartiles and percentiles. ___________ are special cases of _________________ _________ is the 25th​ percentile, ________ is the 50th ​percentile, and _________ is the 75th percentile

QUARTILES are special cases of PERCENTILES. Q1 is the 25th​ percentile, Q2 is the 50th ​percentile, and Q3 is the 75th percentile

Match the plot with a possible description of the sample.

time (in minutes)it takes people to get to work

Use the frequency distribution shown below to construct an expanded frequency distribution. High Temperatures ​(degrees F​) (sample size= add all frequencies) =365

Frequency 18 (class 20-30) Midpoint: (20+30)/2 = 25 Relative frequency: (class frequency/sample size) 18/365 = .05 cumulative frequency: the frequency +all before frequency = 18 ----------------------------------- Frequency 41 (class 31-41) Midpoint: 36 Relative frequency: .11 cumulative frequency: 18+41 =59 ------------------------------------ Frequency 68 Midpoint: 47 Relative frequency: .19 cumulative frequency: 127

Give conclusions that can be drawn from the graph. Select all the conclusions that can be drawn from the graph.

Too-cautious drivers irk drivers the least Tailgaters irk drivers the most

Determine whether the statement is true or false. If it is​ false, rewrite it as a true statement. Class boundaries ensure that consecutive bars of a histogram touch.

True

Determine whether the statement is true or false. If it is​ false, rewrite it as a true statement. The midpoint of a class is the sum of its lower and upper limits divided by two.

the statement is true

Use the ogive to answer parts​ a) through​ d). ​a) What is the cumulative frequency for a weight of 27.5​ pounds? b) What is the weight for which the cumulative frequency is​ 45? c)How many beagles weigh between 22.5 and 29.5​ pounds? ​d) How many beagles weigh more than 30.5​ pounds?

a.) 40 (follow line upand over) b.) 30.5 (follow over and down) c.) 37 (subtract bottom number from higher number) d.) 10 (subtract lower number from final number)

The scores and their percent of the final grade for a statistics student are given. What is the​ student's weighted mean​ score?

sc % weighted 84 10 8.4 84 15 12.6 96 15 14.4 100 25 25 91 35 31.85 weighted mean: 92.25

Both data sets have a mean of 165. One has a standard deviation of​ 16, and the other has a standard deviation of 24. Which data set has which​ deviation? key: 12|8= 128

​(a) has a standard deviation of 24 and​ (b) has a standard deviation of​ 16, because the data in​ (a) have more variability.

The scores and their percents of the final grade for a statistics student are given. An error occurred grading the final exam. Instead of getting 93​, the student scored 87. What is the​ student's new weighted​ mean?

87.1

Use the​ box-and-whisker plot to determine if the shape of the distribution represented is​ symmetric, skewed​ left, skewed​ right, or none of these.

skewed right

Determine whether the statement is true or false. If it is​ false, rewrite it as a true statement. A data set can have the same​ mean, median, and mode.

true

What is the difference between class limits and class​ boundaries?

Class limits are the least and greatest numbers that can belong to the class. Class boundaries are the numbers that separate classes without forming gaps between them. For integer​ data, the corresponding class limits and class boundaries differ by 0.5.

You are applying for a job at two companies. Company A offers starting salaries with mu equals $ 34 comma 000 and sigma equals $ 3 comma 000. Company B offers starting salaries with mu equals $ 34 comma 000 and sigma equals $ 7 comma 000. From which company are you more likely to get an offer of ​$40 comma 000 or​ more?

Company​ B, because data values that lie within one standard deviation from the mean are considered very usual.

The number of credits being taken by a sample of 13​ full-time college students are listed below. Find the​ mean, median, and mode of the​ data, if possible. If any measure cannot be found or does not represent the center of the​ data, explain why. 9 9 12 12 9 10 8 8 8 8 8 8 11

Find the mean. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. 8 8 8 8 8 8 9 9 9 10 11 12 12 mean: 9.2 --------------- Does the mean represent the center of the​ data? The mean represents the center. ---------------- median: 9 Does the median represent the center of the​ data? The median represents the center. ------------------- mode: 8 The​ mode(s) does​ (do) not represent the center because it​ (one) is the smallest data value.

What are some benefits of representing data sets using frequency​ distributions? What are some benefits of using graphs of frequency​ distributions? What are some benefits of using graphs of frequency​ distributions?

It can be easier to identify patterns of a data set by looking at a graph of the frequency distribution.

Determine whether the statement is true or false. If it is​ false, rewrite it as a true statement. It is impossible to have a​ z-score of 0.

The statement is false. A​ z-score of 0 is a standardized value that is equal to the mean.

Use the frequency histogram to complete the following parts. ​(a) Identify the class with the​ greatest, and the class with the​ least, relative frequency. ​(b) Estimate the greatest and least relative frequencies. ​(c) Describe any patterns with the data.

a: 40.5 bar so 39.5- 41.5 (find average from bar before and bar after) b. 48.5 bar; 47.5-49.5 c. .25 d. .01 sample size (n) = 395 (add all x axis)

A student receives the following​ grades, with an A worth 4​ points, a B worth 3​ points, a C worth 2​ points, and a D worth 1 point. What is the​ student's weighted mean grade point​ score? B in 3 three​-credit classes D in 1 three​-credit class A in 1 four​-credit class C in 1 four​-credit class

mean = 2.7

Find the​ mean, median, and mode of the​ data, if possible. If any of these measures cannot be found or a measure does not represent the center of the​ data, explain why. A sample of seven admission test scores for a professional school are listed below. 9.6 9.6 9.6 9.7 10.4 10.6 10.9

mean: 10.7 center ------------ median:9.7 center -------------- mode: 9.6 The​ mode(s) does​ (do) not represent the center because it​ (one) is the smallest data value.

Find the range of the data set represented by the graph. "womens age at first childbirth"

range = 10

Determine whether the statement is true or false. If it is​ false, rewrite it as a true statement. When each data class has the same​ frequency, the distribution is symmetric.

true

rule for SD distributions %

For data sets with distributions that are approximately symmetric and​ bell-shaped, the Empirical Rule states that about​ 68% of the data lie within one standard deviation of the​ mean, about​ 95% of the data lie within two standard deviations of the​ mean, and about​ 99.7% of the data lie within three standard deviations of the mean.

Determine whether the statement is true or false. If it is​ false, rewrite it as a true statement. An ogive is a graph that displays relative frequencies.

The statement is false. An ogive is a graph that displays cumulative frequencies.

Given a data​ set, how do you know whether to calculate sigma or​ s?

When given a data​ set, one would have to determine if it represented the population or if it was a sample taken from the population. If the data are a​ population, then sigma is calculated. If the data are a​ sample, then s is calculated.

Construct the described data set. The entries in the data set cannot all be the same. The median and the mode are the same.

definition of median: The value that lies in the middle of the data when the data set is ordered. ---------------- mode: The data entry that occurs with the greatest frequency. ----------------------- median and mode are equal: 1,1,8,8,8,9,9 ---------------------- A data set includes the entries 3​, 5​, 7​, 9​, 9​, and 12. Complete the data set with an entry between 1 and 12 so that the median and mode of the set are equal. 9

The number of hospital beds in a sample of 20 hospitals is shown below. Construct a frequency distribution and a frequency histogram for the data set using 5 classes. Describe the shape of the histogram as​ symmetric, uniform, negatively​ skewed, positively​ skewed, or none of these. 166 160 126 133 176 157 170 220 149 132 193 204 151 251 267 241 306 142 207 181

Construct a frequency distribution for the data set using 5 classes. ------------------- class freq 126-162 8 163-199 5 200-236 3 237-273 3 274-310 1 --------------------- Describe the shape of the histogram as​ symmetric, uniform, negatively​ skewed, positively​ skewed, or none of these. Choose the correct answer below. The histogram is negatively skewed because the left tail is longer than the right tail.

Construct a frequency distribution and a relative frequency histogram for the accompanying data set using five classes. Which class has the greatest relative frequency and which has the least relative​ frequency? Complete the table below. Use the minimum data entry as the lower limit of the first class.

SumF = 26 class freq relfrq 138-202 14 .538 203-267 4 .154 268-332 4 .154 333-397 1 .038 398-462 3 .115 --------------------- Choose the correct relative frequency histogram below. c graph ---------------- Class has the greatest relative frequency: 138-202 class has the least relative frequency:333-397

Explain the relationship between variance and standard deviation. Can either of these measures be​ negative? Explain.

The standard deviation is the positive square root of the variance. The standard deviation and variance can never be negative. Squared deviations can never be negative.

Determine whether the statement is true or false. If it is​ false, rewrite it as a true statement. Some quantitative data sets do not have medians.

The statement is false. All quantitative data set have medians.

The letters​ A, B, and C are marked on the histogram. Describe the shape of the data. Then determine which is the​ mean, which is the​ median, and which is the mode. Justify your answers.

Which description below best describes the shape of the​ distribution? skewed right ---------------- In this​ distribution, how is the mode​ determined? highest frequency ------------------------ mode = A -------------------- In this​ distribution, how is the mean​ determined? to the right of median and mode ----------------------- mean = C --------------------- In this​ distribution, how is the median​ determined? The median is to the left of the mean and to the right of the mode. ------------------------ Median = B

What is the difference between relative frequency and cumulative​ frequency?

Relative frequency of a class is the percentage of the data that falls in that​ class, while cumulative frequency of a class is the sum of the frequencies of that class and all previous classes.

The ogive represents the heights of males in a particular country in the​ 20-29 age group. What height represents the 70th​ percentile? How should you interpret​ this?

70th percentile is about = 71 Interpret this percentile. Choose the correct answer below. = This means that about 70 percent of males in this country ages​ 20-29 are shorter than this height.

A certain brand of automobile tire has a mean life span of 39 comma 000 miles and a standard deviation of 2 comma 350 miles.​ (Assume the life spans of the tires have a​ bell-shaped distribution.) ​(a) The life spans of three randomly selected tires are 34 comma 000 ​miles, 38 comma 000 ​miles, and 31 comma 000 miles. Find the​ z-score that corresponds to each life span.

34= -2.13 38= -.43 31= -3.40 unusual = yes 36650: z = -1=16% 41350: z=1 = 84% 39000: 50%

Use the ogive to approximate​ (a) the number in the​ sample, (b) the location of the greatest increase in frequency.

a) 50 b) 22.5-23.5

The data show the number of hours spent studying per day by a sample of 28 students. Use the​ box-and-whisker plot below to answer parts​ (a) through​ (c) below. 1 11 5 4 3 0 5 9 6 1 7 4 6 3 1 1 1 9 6 5 2 4 9 2 0 9 3 8

About​ 75% of the students studied no more than how many hours per​ day? = 6.5 What percent of the students studied more than 4 hours per​ day? 50% You randomly select one student from the sample. What is the likelihood that the student studied less than 1.5 hours per​ day? = 25%

Use the dot plot to list the actual data entries. What is the maximum data​ entry? What is the minimum data​ entry?

Choose the correct actual data entries below. 18​, 18​, 19​, 19​, 19​, 20​, 20​, 20​, 20​, 20​, 21​, 22​, 22​, 23​, 24 ------------- max: 24 min:18

Use the​ stem-and-leaf plot to list the actual data entries. What is the maximum data​ entry? What is the minimum data​ entry?

Choose the correct actual data entries below. 26​, 32​, ​41, 43​, 43​, 45​, 46​, 46​, 47​, ​50, 51,​ 51, 52,​ 53, 53,​ 53, 54,​ 54, 54,​ 54, 55,​ 56, 56,​ 58, 59, 67​, 67​, 67​, ​73, 77​, 77​, 83 --------------------- max: 83 min: 26

The accompanying data set lists the numbers of children of world leaders. Use the data to construct a frequency distribution using six classes and to create a frequency polygon. Describe any patterns.

Class Freq mid 0-2 11 1 3-5 13 4 6-8 11 7 9-11 1 10 12-14 2 13 15-17 5 16 ------------------------ Create a frequency polygon. Choose the correct graph below. graph c ------------------------ Describe any patterns. Choose the correct answer below. The data show that most of the 43 world leaders had fewer than 6 children.

The class levels of 32 students in a physics course are shown below. Find the​ mean, median, and mode of the​ data, if possible. If any measure cannot be​ found, explain why. freshman:10 sophmore: 12 junior: 8 senior: 2

Find the mean. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice: The mean cannot be calculated because the data are at the nominal level of measurement. ------------ Does the mean represent the center of the​ data? data does not have a mean ------------ median: The median cannot be calculated because the data are at the nominal level of measurement. no median --------------- mode: sophmores ​Yes, the mode represents a typical data entry.

The ages of the winners of a cycling tournament are approximately​ bell-shaped. The mean age is 27.9 ​years, with a standard deviation of 3.3 years. The winner in one recent year was 34 years old. ​(a) Transform the age to a​ z-score. ​(b) Interpret the results. ​(c) Determine whether the age is unusual.

z=1.85 1.85 above the mean No comma this value is not unusual. A​ z-score between minus 2 and 2 is not unusual.

The data set below represents the ages of 30 executives. Which ages are above the 75th ​percentile? 44 59 64 47 57 40 56 54 60 55 56 50 66 56 50 60 48 40 49 44 55 40 48 45 29 34 39 42 41 44

The ages above the 75th percentile are 57 comma 59 comma 60 comma 60 comma 64 comma 66.

Use the given minimum and maximum data​ entries, and the number of​ classes, to find the class​ width, the lower class​ limits, and the upper class limits. minimum= 12​, maximum=81​, 7 classes

The class width: (81- 12)/ 7 = 10 The lower class limits are: minimum + class width = 12,22,32,42,52,62,72 The upper class limits are: (begin at 1 less thaan the second lower class then add class width) = 21,31,41,51,61,71,81

Without performing any​ calculations, determine which measure of central tendency best represents the graphed data. Explain your reasoning.

The mean is the best measure because there are outliers and the data is skewed.

Determine whether the approximate shape of the distribution in the histogram shown is​ symmetric, uniform, skewed​ left, skewed​ right, or none of these. Justify your answer.

The shape of the distribution is​ symmetric, but not​ uniform, because a vertical line can be drawn down the​ middle, creating two halves that look approximately the same.

Determine whether the statement is true or false. If it is​ false, rewrite it as a true statement. The 50th percentile is equivalent to Upper Q 1.

The statement is false. The 50th percentile is equivalent to Upper Q 2.

The goals scored per game by a soccer team represent the first quartile for all teams in a league. What can you conclude about the​ team's goals scored per​ game?

The team scored fewer goals per game than​ 75% of the teams in the league.

Construct the described data set. The entries in the data set cannot all be the same. The mean is not representative of a typical number in the data set.

What is the definition of​ mean?: The sum of the data entries divided by the number of entries. --------------------- Choose the data set whose mean is not equal to a value in the set. 5,5,6,6

Describe the difference between the calculation of population standard deviation and that of sample standard deviation. Let N be the number of data entries in a population and n be the number of data entries in a sample data set. Choose the correct answer below.

When calculating the population standard​ deviation, the sum of the squared deviation is divided by​ N, then the square root of the result is taken. When calculating the sample standard​ deviation, the sum of the squared deviations is divided by nminus​1, then the square root of the result is taken.

The mean value of land and buildings per acre from a sample of farms is ​$1800​, with a standard deviation of ​$100. The data set has a​ bell-shaped distribution. Using the empirical​ rule, determine which of the following​ farms, whose land and building values per acre are​ given, are unusual​ (more than two standard deviations from the​ mean). Are any of the data values very unusual​ (more than three standard deviations from the​ mean)? $1861 ​$2085 ​$1754 ​$1498 ​$1919 ​$1856 a.) Which of the farms are unusual​ (more than two standard deviations from the​ mean)? Select all that apply. b.) Which of the farms are very unusual​ (more than three standard deviations from the​ mean)? Select all that apply.

a.) $2085 and $1498 b.)$1498

The table shows population statistics for the ages of Best Actor and Best Supporting Actor winners at an awards ceremony. The distributions of the ages are approximately​ bell-shaped. Compare the​ z-scores for the actors in the following situation. Best Actor Best Supporting Actor muequals44.0 muequals50.0 sigmaequals6.9 sigmaequals14 In a particular​ year, the Best Actor was 41 years old and the Best Supporting Actor was 81 years old.

best actor: z= -.41 best supporting: z = 2.21 The Best Actor was less than 1 standard deviation below the​ mean, which is not unusual. The Best Supporting Actor was more than 2 standard deviations above the​ mean, which is unusual.

During a quality assurance​ check, the actual contents​ (in grams) of six containers of protein powder were recorded as 1532​, 1523​, 1498​, 1511​, 1527​, and 1509. ​(a) Find the mean and the median of the contents. ​(b) The third value was incorrectly measured and is actually 1512. Find the mean and the median of the contents again. ​(c) Which measure of central​ tendency, the mean or the​ median, was affected more by the data entry​ error?

mean: 1516.7 median:1517 ------------------ mean:1519 median: 1517.5 ---------------- mean increased by 2.3 and the median increased by .5 so the mean increased more

Use the​ box-and-whisker plot to identify the​ five-number summary.

min = 11 q1 = 12 q2=16 q3= 18 max = 20

The ages​ (in years) of a random sample of shoppers at a gaming store are shown. Determine the​ range, mean,​ variance, and standard deviation of the sample data set. 12​, 17​, 23​, 14​, 13​, 17​, 21​, 17​, 15​, 18

range: 11 mean: 16.7 varience:11.79 (SUM(observerd-mean)^2)/n-1 standard deviation: 3.4 sqrrt(varience)

The numbers of regular season wins for 10 football teams in a given season are given below. Determine the​ range, mean,​ variance, and standard deviation of the population data set. 2​, 7​, 15​, 4​, 11​, 6​, 14​, 9​, 3​, 9

range: 13 mean: 8 varience: (SUM(observerd-mean)^2)/N 17.8 standard deviation: sqrrt(varience) 4.2

In terms of displaying​ data, how is a​ stem-and-leaf plot similar to a dot​ plot? Select all the similarities below.

- Both plots can be used to identify unusual data values. - Both plots can be used to determine specific data entries. - Both plots show how data are distributed.

Match the plot with a possible description of the sample.

Highest yearly temperature of sample deserts

The mean value of land and buildings per acre from a sample of farms is ​$1600​, with a standard deviation of ​$100. The data set has a​ bell-shaped distribution. Assume the number of farms in the sample is 70. a.) Use the empirical rule to estimate the number of farms whose land and building values per acre are between ​$1400 and ​$1800. b.) If 26 additional farms were​ sampled, about how many of these additional farms would you expect to have land and building values between ​$1400 per acre and ​$1800 per​ acre?

a.) 95% of 70 = 67 farms b.)95% of 26 = 25

What is an advantage of using a​ stem-and-leaf plot instead of a​ histogram? What is a​ disadvantage? ------------------- What is a disadvantage of using a​ stem-and-leaf plot instead of a​ histogram?

​Stem-and-leaf plots contain original data values where histograms do not. ----------------------- Histograms easily organize data of all sizes where​ stem-and-leaf plots do not.

Use the frequency histogram to complete the following parts. ​(a) Determine the number of classes. ​(b) Estimate the greatest and least frequencies. ​(c) Determine the class width. ​(d) Describe any patterns with the data.

a: 7 b: 20 c: 275 d: About half of the​ employees' salaries are between ​$50,000 and ​$69,000.

A certain brand of automobile tire has a mean life span of 37 comma 000 miles and a standard deviation of 2 comma 200 miles.​ (Assume the life spans of the tires have a​ bell-shaped distribution.) The life spans of three randomly selected tires are 34 comma 000 ​miles, 38 comma 000 ​miles, and 31 comma 000 miles. Find the​ z-score that corresponds to each life span.

34000 mile z = -1.36 38000 mile z = .45 31000 mile z = -2.73 -yes one would be unusual --------------------------------- The life spans of three randomly selected tires are 34 comma 800 ​miles, 39 comma 200 ​miles, and 37 comma 000 miles. Using the empirical​ rule, find the percentile that corresponds to each life span. 34800 %= 16 39200 %= 84 37000 % = 50 (68% 1 SD from mean, 95 2SD and 99.7 3 SD from mean) When a distribution is approximately​ bell-shaped, the empirical rule says that​ 68% of the data lie within one standard of the​ mean, 95% of the data lie within two standard deviations of the​ mean, and​ 99.7% of the data lie within three standard deviations of the mean.​ So, when this​ distribution's values are transformed to​ z-scores, about​ 68% of the​ z-scores should fall between minus1 and​ 1, about​ 95% should fall between minus2 and​ 2, and about​ 99.7% should fall between minus3 and 3. Transform each value to a​ z-score, and use the empirical rule to find the percentage of tires that have a life span at or below each life span.

Use the frequency histogram to complete the following parts. ​(a) Determine the number of classes. ​(b) Estimate the greatest and least frequencies. ​(c) Determine the class width. ​(d) Describe any patterns with the data.

A) number of classes: 7 (count x axis) B) least frequency: 20 (estemate height of lowest bar) C) Greatest frequency: 300 (height of tallest bar) class width: 37-32 = 5 D) What is the pattern of this histogram? About half of the​ employees' salaries are between ​$40,000 and ​$49,000.

The acccompanying data set lists the retirement ages for 24 doctors. Use the data to construct a cumulative frequency distribution using six classes and to create an ogive for the data set. Then describe the location of the greatest increase in frequency.

class freq cumfre 50-54 2 2 55-59 4 6 60-64 4 10 65-69 9 19 70-74 2 21 75-79 3 24 ------------------- Create an ogive for the data set. Choose the correct graph below. graph D ---------- Where does the greatest increase in cumulative frequency​ occur? The location of the greatest increase in cumulative frequency is at class 65-69 (plae of largest cumulative frequency

The data represent the​ time, in​ minutes, spent reading a political blog in a day. Construct a frequency distribution using 5 classes. In the​ table, include the​ midpoints, relative​ frequencies, and cumulative frequencies. Which class has the greatest frequency and which has the least​ frequency? Complete the​ table, starting with the lowest class limit. 19 12 7 10 18 4 11 17 3 11 9 17 8 7 0 5 10 9 1 9

class: 0-3 frequency: 3 midpoint: 1.5 relative frequency:.15 cumulative frequency: 3 ------------------------------- class: 4-7 frequency: 4 midpoint: 5.5 relative frequency: .20 cumulative frequency: 7 ------------------------------- class: 8-11 frequency: 8 midpoint: 9.5 relative frequency:.4 cumulative frequency: 15 ------------------------------- class: 12-15 frequency: 1 midpoint: 13.5 relative frequency:.05 cumulative frequency: 16 ------------------------------- class:16-19 frequency: 4 midpoint: 17.5 relative frequency: .2 cumulative frequency: 20 _________________________________________________ Which class has the greatest frequency? 8-11 ------------------------------------ least frequency? 12-15


Ensembles d'études connexes

BSA 13 Office of Foreign Asset Control OFAC

View Set

Intermediate Spanish I Chapter 1

View Set

Chapter 14 Providing Employee Benefits

View Set

Chp 4 Interpersonal Communication Homework and Exam

View Set

Computer Programming C++ Chapter Four

View Set

Chp. 32: Fetal Environment and Maternal Complications

View Set

Adult Health 2 Final Exam Review

View Set