Q: Which formula would you use to find the percentile rank of a data value $$x in a $$data set?

$$\text{Percentile rank} = \frac{\text{number of values} \leq x}{n} \times 100$$

Question 1

Given the following data set representing the number of music videos released by four performers: 31, 26, 26, 15. What is the mode of this data set?

Accepted Answer

26

Question 2

Which measure of central tendency is most appropriate to use when a data set is highly skewed right?

Accepted Answer

Median

Question 3

A data set has a mean of 50 and a median of 60. Based on this information, what is the most likely shape of the distribution?

Accepted Answer

Skewed left

Question 4

Given the following data: 23, 36, 23, 18, 5, 26, 43. Calculate the population mean. Use $$\mu = \frac{\sum x_i}{N}.$$

Accepted Answer

$$\mu = 24.86$$

Question 5

Which of the following statements about the standard deviation is TRUE?

Accepted Answer

It measures the spread of the data around the mean.

Question 6

For the data set: 5, 26, 36, the sample standard deviation is calculated as $$s = \sqrt{\frac{\sum x_i^2$ - (\sum x_i)^2$/n}{n-1}}. $$What is the value of $$s$$?

Accepted Answer

$$s \approx 15.82$$

Question 7

A bell-shaped distribution has a mean of 514 and a standard deviation of 118. According to the Empirical Rule, approximately what percentage of data falls between 396 and 632?

Accepted Answer

68%

Question 8

Chebyshev’s Rule states that for any data set, at least what percentage of values fall within 2 standard deviations of the mean?

Accepted Answer

75%

Question 9

A student scored 650 on a Math SAT where the mean is 500 and the standard deviation is 100. What is the student’s z-score? Use $$z = \frac{x - \mu}{\sigma}.$$

Accepted Answer

$$z = 1.5$$

Question 10

Which of the following is NOT part of the five-number summary?

Accepted Answer

Mean

Question 11

Given the following ordered data set: 1.6, 2.7, 3.3, 3.5, 3.5, 4.6, 4.7, 4.8, 5.0, 5.8, 7.5, 7.7. What is the value of the third quartile (Q3)?

Accepted Answer

5.4

Question 12

If a data value is more than 1.5 times the interquartile range (IQR) above Q3, what is it considered?

Accepted Answer

An outlier

Question 13

Which of the following best describes a distribution where the mean is substantially larger than the median?

Accepted Answer

Skewed right

Question 14

A boxplot shows the median closer to the lower quartile (Q1) than to the upper quartile (Q3). What does this suggest about the distribution?

Accepted Answer

The distribution is skewed right.

Question 15

Which measure of spread is most robust (least affected by outliers)?

Accepted Answer

Interquartile range (IQR)

Question 16

Given a data set with minimum = 20, Q1 = 28, median = 32.5, Q3 = 38, and maximum = 40, what is the interquartile range (IQR)?

Accepted Answer

IQR = 6

Question 17

If a data set has no repeated values, what can be said about its mode?

Accepted Answer

There is no mode.

Question 18

Which formula would you use to find the percentile rank of a data value $$x in a $$data set?

Accepted Answer

$$	ext{Percentile rank} = \frac{	ext{number of values} \leq x}{n} 	imes 100$$

Question 19

Which of the following is a resistant measure of center?

Accepted Answer

Median

Numerically Summarizing Data: Measures of Central Tendency, Dispersion, Position, and Boxplots

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