Q: What is the formula for the midpoint of a class in a frequency distribution?

$$\text{Midpoint} = \frac{\text{Lower class limit} + \text{Upper class limit}}{2}$$

Q: A sample of 10 salaries has a mean of $$50,000$$ and a standard deviation of $$5,000. $$What is the coefficient of variation (CV) as a percentage?

$$CV = \frac{5,000}{50,000} \times 100\% = 10\%$$

Question 1

Which of the following best describes the purpose of a frequency distribution in statistics?

Accepted Answer

To organize data into classes or intervals and show the number of entries in each class.

Question 2

Given a data set with a minimum value of 12 and a maximum value of 52, you want to create 8 classes for a frequency distribution. What is the appropriate class width?

Accepted Answer

$$\frac{52-12}{8} = 5 (so $$use 6 as the class width, rounding up)

Question 3

What is the formula for the midpoint of a class in a frequency distribution?

Accepted Answer

$$	ext{Midpoint} = \frac{	ext{Lower class limit} + 	ext{Upper class limit}}{2}$$

Question 4

A frequency histogram must have which of the following properties?

Accepted Answer

Bars must touch each other to represent continuous data.

Question 5

If a data set has the following values: 3, 7, 7, 8, 10, what is the mode?

Accepted Answer

7

Question 6

Which measure of central tendency is most affected by an outlier in a data set?

Accepted Answer

Mean

Question 7

A sample of exam scores is: 70, 75, 80, 85, 90. What is the sample mean?

Accepted Answer

$$\frac{70+75+80+85+90}{5} = 80$$

Question 8

Which of the following best describes a symmetric distribution?

Accepted Answer

The left and right halves of the distribution are mirror images.

Question 9

The Empirical Rule states that for a bell-shaped distribution, approximately what percent of data falls within two standard deviations of the mean?

Accepted Answer

95%

Question 10

Given a population with mean $$\mu = 50$$ and standard deviation $$\sigma = 5$$, what is the z-score for a value $$x = 60$$?

Accepted Answer

$$z = \frac{60-50}{5} = 2$$

Question 11

Which of the following is the correct formula for the sample variance $$s^2$$?

Accepted Answer

$$s^2$$ = \frac{\sum (x - \overline{x}$$)^2$$}{n-1}$$

Question 12

A data set has $$Q_1 = 20$, Q_3$ = 40. $$What is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 20$$

Question 13

If a value is more than $$Q_3 + 1.5$$ 	imes IQR$$, what can you conclude?

Accepted Answer

It is an outlier.

Question 14

Which type of graph is best for displaying the cumulative frequency of a data set?

Accepted Answer

Ogive

Question 15

A sample of 10 salaries has a mean of $$50,000$$ and a standard deviation of $$5,000. $$What is the coefficient of variation (CV) as a percentage?

Accepted Answer

$$CV = \frac{5,000}{50,000} 	imes 100\% = 10\%$$

Question 16

Which of the following is NOT a property of the standard deviation?

Accepted Answer

It is resistant to outliers.

Question 17

A box-and-whisker plot requires which of the following five-number summary values?

Accepted Answer

Minimum, $$Q_1$$, Median, $$Q_3$$, Maximum

Question 18

If a data set is skewed right, which of the following is true?

Accepted Answer

The mean is greater than the median.

Question 19

Which formula is used to find the percentile rank of a data entry $$x in a $$data set?

Accepted Answer

$$	ext{Percentile of } x = \frac{	ext{number of values less than } x}{	ext{total number of values}} 	imes 100$$

Descriptive Statistics: Frequency Distributions and Their Graphs

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