Q: Given the following frequency distribution of no-shows for airline flights: 0 (37), 1 (31), 2 (20), 3 (16), 4 (12), 5 (4). What is the mean number of no-shows per flight?

$$\frac{(0 \times 37) + (1 \times 31) + (2 \times 20) + (3 \times 16) + (4 \times 12) + (5 \times 4)}{37 + 31 + 20 + 16 + 12 + 4} = 1.56$$

Q: Which of the following is the formula for the coefficient of variation (CV) for a sample?

$$CV = \frac{s}{\bar{x}} \times 100$$

Question 1

A company tracks the weights of cereal boxes produced by a machine. The standard is 18 kg per box. A sample of five boxes has weights: 13.1, 14.2, 19.6, 20.9, and 22.7 kg. What is the sample mean weight of these boxes?

Accepted Answer

$$\frac{13.1 + 14.2 + 19.6 + 20.9 + 22.7}{5} = 18.1$$

Question 2

Which measure of central tendency is most appropriate to describe the center of a data set with significant outliers?

Accepted Answer

Median

Question 3

A sample of home prices is: $$100,000, 100$$,000, $$300,000, 500$$,000, $2,000,000. What is the median price?

Accepted Answer

$$300,000$$

Question 4

Given the following frequency distribution of no-shows for airline flights: 0 (37), 1 (31), 2 (20), 3 (16), 4 (12), 5 (4). What is the mean number of no-shows per flight?

Accepted Answer

$$\frac{(0 	imes 37) + (1 	imes 31) + (2 	imes 20) + (3 	imes 16) + (4 	imes 12) + (5 	imes 4)}{37 + 31 + 20 + 16 + 12 + 4} = 1.56$$

Question 5

Which of the following is NOT a disadvantage of using the mean to summarize data?

Accepted Answer

It is difficult to calculate

Question 6

A data set has a mean of 50 and a standard deviation of 20. What is the z-score for a value of 70?

Accepted Answer

$$z = \frac{70 - 50}{20} = 1$$

Question 7

If a distribution is right-skewed, which of the following is true about the relationship between the mean and the median?

Accepted Answer

Mean \u003e Median

Question 8

A sample has a mean of 776.3 and a standard deviation of 385.1. What is the z-score for a value of 540?

Accepted Answer

$$z = \frac{540 - 776.3}{385.1} = -0.61$$

Question 9

According to the Empirical Rule, approximately what percentage of data falls within two standard deviations of the mean in a bell-shaped distribution?

Accepted Answer

95%

Question 10

A company has two stores. Store A has a mean customer satisfaction rating of 5.8 and a standard deviation of 2.39. Store B has a mean of 8.2 and a standard deviation of 1.1. Which store is more consistent in customer satisfaction?

Accepted Answer

Store B, because it has a lower coefficient of variation

Question 11

Which formula is used to calculate the sample variance?

Accepted Answer

$$s^2$$ = \frac{\sum_{i=1}^n (x_i - \bar{x}$$)^2$$}{n-1}$$

Question 12

Given a data set: 11, 12, 13, 16, 16, 17, 18, 21, 22, 22, 25. What is the value of the first quartile (Q1)?

Accepted Answer

13

Question 13

Which of the following best describes the interquartile range (IQR)?

Accepted Answer

The difference between the third and first quartiles

Question 14

A boxplot shows a median near the left edge of the box and a longer right whisker. What does this indicate about the distribution?

Accepted Answer

The distribution is right-skewed

Question 15

If a value is more than 1.5 times the IQR above Q3 or below Q1, what is it considered?

Accepted Answer

An outlier

Question 16

Which Excel function would you use to calculate the sample standard deviation for a data set in column A from row 2 to row 10?

Accepted Answer

=STDEV.S(A2:A10)

Question 17

A histogram of store sales is highly right-skewed with several high outliers. Which measure best summarizes the center of the data?

Accepted Answer

Median

Question 18

Which of the following is the formula for the coefficient of variation (CV) for a sample?

Accepted Answer

$$CV = \frac{s}{\bar{x}} 	imes 100$$

Question 19

According to Chebyshev’s Theorem, at least what percentage of data falls within 2 standard deviations of the mean for any distribution?

Accepted Answer

75%

Chapter 3

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드