Q: Which formula is used to find the percentile rank of a value $$x in a $$data set of size $$n$$?

$$\frac{\text{number of values less than } x}{n} \times 100$$

Question 1

Which of the following best describes the mean of a data set?

Accepted Answer

The sum of all values divided by the number of values.

Question 2

Given the sample data set $$\{5, 10, 12, 14, 13, 12, 11\}$$, what is the mean?

Accepted Answer

$$12$$

Question 3

A sample of home prices (in thousands of dollars) is $$\{375, 225, 200, 240, 300, 287, 301, 342\}. $$Which measure is more representative of the typical home price if one home is much more expensive than the others?

Accepted Answer

The median, because it is less affected by outliers.

Question 4

Which formula correctly calculates the sample standard deviation $$s$$ for a data set $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

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

Question 5

A hospital records the birth weights of newborns with a mean of $$3.5 kg $$and a standard deviation of $$0.4 kg. $$According to the Empirical Rule, what percentage of newborns have weights between $$2.7 kg $$and $$4.3 kg$$?

Accepted Answer

$$68\%$$

Question 6

Which of the following is true about the mode?

Accepted Answer

It can be used for both quantitative and qualitative data.

Question 7

A data set has the following values: $$\{10, 12, 14, 16, 18, 20, 22\}. $$What is the median?

Accepted Answer

$$16$$

Question 8

If a data set is symmetric and has no outliers, which measure of center is generally preferred?

Accepted Answer

Mean

Question 9

The five-number summary consists of which of the following values?

Accepted Answer

Minimum, Q1, Median, Q3, Maximum

Question 10

A set of exam scores is normally distributed with a mean of $$80$$ and a standard deviation of $$5. $$According to the Empirical Rule, what is the range of scores that contains approximately $$95\% of $$the data?

Accepted Answer

$$70 to$$ $$90$$

Question 11

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

Accepted Answer

The difference between the first and third quartiles.

Question 12

A histogram of college credits per semester is right-skewed. Which measure of center is most likely to be greater?

Accepted Answer

The mean

Question 13

If a data set has more than one mode, it is called:

Accepted Answer

Bimodal or Multimodal

Question 14

Given the data set $$\{2, 4, 4, 4, 5, 6, 7\}$$, what is the mode?

Accepted Answer

$$4$$

Question 15

A sample of 250 wait times at a restaurant has a mean of 6 minutes and a standard deviation of 2.5 minutes. According to the Empirical Rule, what percentage of wait times are expected to be between 3.5 and 8.5 minutes?

Accepted Answer

$$68\%$$

Question 16

Which of the following is NOT a measure of center?

Accepted Answer

Standard deviation

Question 17

If the mean is much greater than the median in a data set, the distribution is likely:

Accepted Answer

Right-skewed

Question 18

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

Accepted Answer

$$\frac{	ext{number of values less than } x}{n} 	imes 100$$

Question 19

A boxplot is useful for displaying:

Accepted Answer

The five-number summary

Question 20

Which of the following statements about standard deviation is correct?

Accepted Answer

A larger standard deviation means the data values are more spread out.

Numerically Summarizing Data: Measures of Center, Variation, and Position

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