Q: A student scored 82 on a test. If 40 students scored lower than 82 out of a total of 50 students, what is the percentile rank of the student?

$$\frac{40}{50} \times 100 = 80th $$percentile

Q: A data set has $$Q_1 = 47$, Q_3$ = 58.5$$, and $$IQR = 11.5. $$Which value would be considered an outlier?

A value less than $$Q_1 - 1.5($$IQR) = 47 - 1.5 \times 11.5 = 29.75$$

Question 1

A researcher collects the daily screen time (in minutes) for 30 students and organizes the data into a frequency distribution with 7 classes. If the minimum value is 155 and the maximum is 405, what is the appropriate class width to use?

Accepted Answer

$$\frac{405-155}{7} = 35.71$$, so round up to 36$

Question 2

Which of the following best describes the difference between a histogram and a bar chart?

Accepted Answer

A histogram displays frequencies of quantitative data with adjacent bars, while a bar chart displays frequencies of categorical data with separated bars.

Question 3

Given the following data set: 23, 35, 35, 40, 42, 42, 42, 50, what is the mode?

Accepted Answer

42

Question 4

A sample of 12 concussion recovery times (in days) has a mean of 7.5 days and a sum of squared deviations $$\sum (x-\bar{x})^2$ = 55. $$What is the sample variance?

Accepted Answer

$$s^2$$ = \frac{55}{11} = 5$$

Question 5

Which of the following is NOT a property of the mean?

Accepted Answer

It is always equal to the median in a skewed distribution.

Question 6

A data set has a minimum value of 19, a first quartile $$Q_1 of 47$$, a median of 55, a third quartile $$Q_3 of 58.5$$, and a maximum of 61. What is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 58.5 - 47 = 11.5$$

Question 7

If a data set is bell-shaped and has a mean of 100 and a standard deviation of 15, according to the Empirical Rule, approximately what percentage of data falls between 85 and 115?

Accepted Answer

About 68%

Question 8

A student scored 82 on a test. If 40 students scored lower than 82 out of a total of 50 students, what is the percentile rank of the student?

Accepted Answer

$$\frac{40}{50} 	imes 100 = 80th $$percentile

Question 9

Which of the following statements about standard deviation is TRUE?

Accepted Answer

Standard deviation is always greater than or equal to zero.

Question 10

A frequency distribution for cell phone screen times has the following class: 227-262 minutes, with a frequency of 5. What is the class midpoint?

Accepted Answer

$$\frac{227 + 262}{2} = 244.5$$

Question 11

Which of the following is the correct formula for the sample mean $$\bar{x} of a $$frequency distribution with midpoints $$x$$ and frequencies $$f$$?

Accepted Answer

$$\bar{x} = \frac{\sum f x}{\sum f}$$

Question 12

A box-and-whisker plot is constructed for a data set. Which of the following is NOT part of the five-number summary?

Accepted Answer

The mean

Question 13

A data set has $$Q_1 = 47$, Q_3$ = 58.5$$, and $$IQR = 11.5. $$Which value would be considered an outlier?

Accepted Answer

A value less than $$Q_1 - 1.5($$IQR) = 47 - 1.5 	imes 11.5 = 29.75$$

Question 14

Which of the following best describes a negatively skewed (left-skewed) distribution?

Accepted Answer

The mean is less than the median, and the tail is longer on the left.

Question 15

A time series chart is most appropriate for which type of data?

Accepted Answer

Data collected at regular intervals over time

Question 16

If the range of a data set is 42 and the minimum value is 19, what is the maximum value?

Accepted Answer

61

Question 17

Which of the following is the correct formula for the population standard deviation $$\sigma$$?

Accepted Answer

$$\sigma = \sqrt{\frac{\sum (x - \mu)^2$}{N}}$$

Question 18

A pie chart is most appropriate for displaying which type of data?

Accepted Answer

Categorical data showing proportions of a whole

Question 19

A sample of 50 households has the following frequency distribution for number of children: 0 children (10), 1 child (19), 2 children (7), 3 children (7), 4 children (2), 5 children (1), 6 children (4). What is the mean number of children per household?

Accepted Answer

$$\bar{x} = \frac{0 	imes 10 + 1 	imes 19 + 2 	imes 7 + 3 	imes 7 + 4 	imes 2 + 5 	imes 1 + 6 	imes 4}{50} = \frac{91}{50} = 1.82$$

Descriptive Statistics: Frequency Distributions, Graphs, and Measures Chapter. 2

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