Unit 3 Statistics

Winston has just gone grocery shopping. The mean cost for each item in his bag was $3.40$⁢3.40. He bought a total of 99 items, and the prices of 88 of those items are listed below: $3.11,$4.04,$3.99,$3.79,$2.29,$2.53,$2.81,$4.30$⁢3.11,$⁢4.04,$⁢3.99,$⁢3.79,$⁢2.29,$⁢2.53,$⁢2.81,$⁢4.30 Determine the price of the 99th item in his bag. Copy Data

$3.74

Consider a set of data in which the sample mean is 35.135.1 and the sample standard deviation is 6.96.9. Calculate the z-score given that x=29.7�=29.7. Round your answer to two decimal places.

-.078

Given the following graph, where the mean is marked, which value best represents the z-score shown? z0

-1.9

Consider the following box plots for Data Set A and Data Set B. 45455050555560606565707075758080858590909595∞∞−∞−∞93934848565677.577.58383Data Set A 45455050555560606565707075758080858590909595∞∞−∞−∞88885353585869698181Data Set B Which data set has the largest variation?

data set a

Consider the following data. 10,15,9,12,14,610,15,9,12,14,6 Copy Data Determine if the data set is unimodal, bimodal, multimodal, or has no mode. Identify the mode(s), if any exist.

no mode

Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to one more decimal place than the largest number of decimal places given in the data. 5,5,5,5,5,5,5,5,5,5

range=0 pop. variance=0 pop. standard dev.=0

Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to one more decimal place than the largest number of decimal places given in the data. 10,9,4,3,7,6,4,5,3,34

range=31 pop. variance=77.45 standard dev.=8.80

Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to one more decimal place than the largest number of decimal places given in the data. 4,5,6,7,8,9,10,11,12,134,5,6,7,8,9,10,11,12,13 Copy Data

range=9 pop. variance=8.3 standard dev.=2.9

Select the word or phrase that will correctly complete the statement. A/An measures the number of standard deviations that a particular value is away from the mean.

z-score

Given the following data, find the diameter that represents the 38th percentile. Diameters of Golf Balls1.531.351.331.581.581.541.371.671.611.531.311.421.341.551.36 Copy Data

1.37

Amy is looking into investing a portion of her recent bonus into the stock market. While researching different companies, she discovers the following standard deviations of one year of daily stock closing prices. The Azure Travel Company: Standard deviation of stock prices =$1.22=$⁢1.22 El Lobo Malo Incorporated: Standard deviation of stock prices =$9.72=$⁢9.72 Based on the data and assuming these trends continue, which company would give Amy a stable long-term investment?

The Azure travel company; the smaller standard deviation indicates that the company has less variability than in its closing prices than El Lobo Malo incorporated.

Consider the following data. 2,8,8,8,2,−2,22,8,8,8,2,−2,2 Copy Data Determine if the data set is unimodal, bimodal, multimodal, or has no mode. Identify the mode(s), if any exist.

bimodal= 2;8

Find the mean, median, and mode of the following data. If necessary, round to one more decimal place than the largest number of decimal places given in the data. MLB Batting Averages0.2910.2910.3200.3200.2740.2740.2990.2990.3120.3120.3180.3180.3240.3240.2990.2990.3100.3100.2920.2920.2960.2960.2850.2850.2790.2790.2900.2900.2760.2760.2770.2770.3160.3160.3210.3210.3070.3070.3010.301 Copy Data

Mean= 0.29935 Median=0.299 Mode=0.299

or the following type of data set, would you be more interested in looking at the mean, median, or mode? State your reasoning. The color of car preferred by American males. First, select the correct measure of center and then select the justification for your choice.

Measure =mode; Justification=the preferred colors are qualitative data

Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to one more decimal place than the largest number of decimal places given in the data. 10,11,14,19,19,11,10,11,6,1510,11,14,19,19,11,10,11,6,15 Copy Data

Range=13 population variance=15.4 Population Standard Deviation=3.9

onsider the following sets of sample data: A: 2.62.6, 3.83.8, 2.62.6, 4.04.0, 1.91.9, 1.81.8, 4.34.3, 2.22.2, 1.91.9, 2.02.0, 4.44.4, 4.44.4, 3.03.0, 3.83.8 B: $2.64$⁢2.64, $2.18$⁢2.18, $1.92$⁢1.92, $2.31$⁢2.31, $2.64$⁢2.64, $1.40$⁢1.40, $1.82$⁢1.82, $1.68$⁢1.68, $2.51$⁢2.51, $1.29$⁢1.29, $2.34$⁢2.34 Copy Data For each of the above sets of sample data, calculate the coefficient of variation, CV. Round to one decimal place.

set A=33.6 Set B=23.1

Consider the following data. 10,15,9,12,14,610,15,9,12,14,6 Copy Data Determine the mean of the given data.

11

Consider the following data. 10,15,9,12,14,610,15,9,12,14,6 Copy Data Determine the median of the given data.

11

Consider the following data: 15,14,10,6,8,715,14,10,6,8,7 Copy Data Calculate the value of the sample variance. Round your answer to one decimal place.

14

Consider the following data. 2,8,8,8,2,−2,22,8,8,8,2,−2,2 Copy Data Determine the mean of the given data.

4

A manufacturer makes bags of popcorn and bags of potato chips. The average weight of a bag of popcorn is supposed to be 3.023.02 ounces with an allowable deviation of 0.030.03 ounces. The average weight of a bag of potato chips is supposed to be 5.015.01 ounces with an allowable deviation of 0.020.02 ounces. A factory worker randomly selects a bag of popcorn from the assembly line and it has a weight of 3.033.03 ounces. Then the worker randomly selects a bag of potato chips from the assembly line and it has a weight of 5.035.03 ounces. Which description closely matches the findings on the assembly line?

The popcorn bag assembly line is closer to the specifications given because its z-score is closer to the standard than the potato chip bag assembly line.

Consider the following box plots for Data Set A and Data Set B. 45455050555560606565707075758080858590909595∞∞−∞−∞94945252686881819090Data Set A 45455050555560606565707075758080858590909595∞∞−∞−∞88884747555564647878Data Set B Which data set has the largest value?

data set A

Consider the following box plots for Data Set A and Data Set B. 45455050555560606565707075758080858590909595∞∞−∞−∞95955858666673738181Data Set A 45455050555560606565707075758080858590909595∞∞−∞−∞87874646545461618181Data Set B Which data set has the largest value?

data set A

Consider the following sets of sample data: A: 2.62.6, 3.83.8, 2.62.6, 4.04.0, 1.91.9, 1.81.8, 4.34.3, 2.22.2, 1.91.9, 2.02.0, 4.44.4, 4.44.4, 3.03.0, 3.83.8 B: $2.64$⁢2.64, $2.18$⁢2.18, $1.92$⁢1.92, $2.31$⁢2.31, $2.64$⁢2.64, $1.40$⁢1.40, $1.82$⁢1.82, $1.68$⁢1.68, $2.51$⁢2.51, $1.29$⁢1.29, $2.34$⁢2.34 Copy Data Which of the above sets of sample data has the larger spread?

data set A

Question 12 of 12 Step 1 of 1 Time Taken: 37 Secs A high school has 3636 players on the football team. The summary of the players' weights is given in the box plot. What is the median weight of the players? 150150160160170170180180190190200200210210220220230230240240250250260260270270∞

192 lbs

Consider the following data. 2,8,8,8,2,−2,22,8,8,8,2,−2,2 Copy Data Determine the median of the given data.

2

Consider the following data: 1,1,−12,10,10,10,11,1,−12,10,10,10,1 Copy Data Calculate the value of the range.

22

Consider the following data: 15,14,10,6,8,715,14,10,6,8,7 Copy Data Calculate the value of the sample standard deviation. Round your answer to one decimal place.

3.7

The following stem-and-leaf plot represents the times in minutes required for 1818 co-workers to commute to work. Use the data provided to find the quartiles. Commute Times in MinutesStemLeaves22226633112244555555440011222277995500557777 Key: 2|2=222|2=22 Copy Data Find the first quartile.

34

The following stem-and-leaf plot represents the times in minutes required for 1818 co-workers to commute to work. Use the data provided to find the quartiles. Commute Times in MinutesStemLeaves22226633112244555555440011222277995500557777 Key: 2|2=222|2=22 Copy Data

40.5

The following stem-and-leaf plot represents the times in minutes required for 1818 co-workers to commute to work. Use the data provided to find the quartiles. Commute Times in MinutesStemLeaves22226633112244555555440011222277995500557777 Key: 2|2=222|2=22 Copy Data

49

A high school has 4444 players on the football team. The summary of the players' weights is given in the box plot. Approximately, what is the percentage of players weighing greater than or equal to 227227 pounds? 150150160160170170180180190190200200210210220220230230240240250250260260270

50%

Consider the following data: 1,1,−12,10,10,10,11,1,−12,10,10,10,1 Copy Data Calculate the value of the sample variance. Round your answer to one decimal place.

64

Consider the following data: 1,1,−12,10,10,10,11,1,−12,10,10,10,1 Copy Data Calculate the value of the sample standard deviation. Round your answer to one decimal place.

8

Three potential employees took an aptitude test. Each person took a different version of the test. The scores are reported below. Reyna got a score of 75.375.3; this version has a mean of 69.369.3 and a standard deviation of 1212. Kaitlyn got a score of 228.4228.4; this version has a mean of 206206 and a standard deviation of 2828. Cade got a score of 7.887.88; this version has a mean of 7.27.2 and a standard deviation of 0.40.4. If the company has only one position to fill and prefers to fill it with the applicant who performed best on the aptitude test, which of the applicants should be offered the job?

Cade

Consider the following box plots for Data Set A and Data Set B. 45455050555560606565707075758080858590909595∞∞−∞−∞94944545626283.583.58989Data Set A 45455050555560606565707075758080858590909595∞∞−∞−∞89895252696973738282Data Set B Which data set has the smallest variation?

data set B

Consider the following data. −14,5,3,−15,−4,1−14,5,3,−15,−4,1 Copy Data Determine the mean of the given data.

-4

Calculate the five-number summary of the given data. Use the approximation method. 7,9,21,1,12,18,21,23,12,17,9,11,6,3,8

1,7,11,18,23

Consider the following data: 15,14,10,6,8,715,14,10,6,8,7 Copy Data Calculate the value of the range.

9

Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.612.61 and a standard deviation of 0.440.44. Using the empirical rule, what percentage of the students have grade point averages that are at least 1.731.73? Please do not round your answer.

97.5%

Suppose that IQ scores have a bell-shaped distribution with a mean of 104104 and a standard deviation of 1818. Using the empirical rule, what percentage of IQ scores are between 5050 and 158158?

99.7%

Suppose that IQ scores have a bell-shaped distribution with a mean of 9696 and a standard deviation of 1313. Using the empirical rule, what percentage of IQ scores are no more than 5757? Please do not round your answer.

0.15%

Calculate the sample standard deviation for the following data set. If necessary, round to one more decimal place than the largest number of decimal places given in the data. Body Temperatures (in ºF) of Adult Females96.796.799.799.799.999.999.399.398.598.598.298.298.098.098.398.3100.2100.298.498.4100.8100.898.798.796.496.4100.8100.899.399.3100.6100.699.499.498.098.099.399.3100.5100.5 Copy Data

1.263

Suppose that prices of a gallon of milk at various stores in one town have a mean of $3.91$⁢3.91 with a standard deviation of $0.13$⁢0.13. Using Chebyshev's Theorem, what is the minimum percentage of stores that sell a gallon of milk for between $3.65$⁢3.65 and $4.17$⁢4.17? Round your answer to one decimal place.

75%

Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.068.06 and a standard deviation of 1.521.52. Using the empirical rule, what percentage of American women have shoe sizes that are less than 9.589.58? Please do not round your answer.

84.13%