Question 1

Which of the following statements best describes a resistant statistic?

Accepted Answer

A statistic that is not affected substantially by extreme values (very large or small) relative to the data.

Question 2

Given the following exam scores: 82, 77, 90, 71, 62, 68, 74, 84, 94, 88, what is the population mean $$\mu$$?

Accepted Answer

$$\mu = \frac{790}{10} = 79$$

Question 3

If a data set has an odd number of observations, how is the median determined?

Accepted Answer

The median is the value exactly in the middle of the ordered data set.

Question 4

A distribution is skewed right. Which measure of central tendency is most likely to be greater?

Accepted Answer

The mean is substantially greater than the median.

Question 5

Which scenario best illustrates when the median is a better measure of central tendency than the mean?

Accepted Answer

A data set with a few extreme values (outliers) skewing the distribution.

Question 6

What is the formula for the sample standard deviation $$s$$?

Accepted Answer

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

Question 7

If the mean IQ score at two universities is 100, but University A has a standard deviation of 16.1 and University B has a standard deviation of 8.4, what can you conclude?

Accepted Answer

University A's IQ scores are more dispersed than University B's.

Question 8

According to the Empirical Rule, what percentage of data in a bell-shaped distribution lies within 2 standard deviations of the mean?

Accepted Answer

Approximately 95%

Question 9

Chebyshev’s Inequality states that for any data set, at least what percentage of observations lie within $$k$$ standard deviations of the mean (where $$k \u003e 1$$)?

Accepted Answer

$$1 - \frac{1}{k^2$}$$

Question 10

A student’s SAT score is in the 74th percentile. What does this mean?

Accepted Answer

74% of students scored less than or equal to this score.

Question 11

What is the formula for the z-score of a sample data value $$x$$?

Accepted Answer

$$z = \frac{x - \bar{x}}{s}$$

Question 12

How is the interquartile range (IQR) calculated?

Accepted Answer

$$IQR = Q_3$ - Q_1$

Question 13

Which of the following is NOT a characteristic used to describe a distribution?

Accepted Answer

Color

Question 14

A boxplot is constructed using which five values?

Accepted Answer

Minimum, Q1, Median, Q3, Maximum

Question 15

If a data value is less than $$Q_1 - 1.5($$IQR)$$ or greater than Q_3$ + 1.5(IQR)$$, what is it considered?

Accepted Answer

An outlier

Question 16

Which formula is used to approximate the mean from grouped data?

Accepted Answer

$$\bar{x} = \frac{\sum x_i f_i}{\sum f_i}$$

Question 17

Which measure of dispersion is most resistant to extreme values?

Accepted Answer

Interquartile range (IQR)

Question 18

A weighted mean is calculated by:

Accepted Answer

Multiplying each value by its weight, summing these products, and dividing by the sum of the weights.

Question 19

If a distribution is bell-shaped and the mean and median are close in value, which measure of central tendency should be used?

Accepted Answer

Mean

Question 20

Which of the following best describes the mode?

Accepted Answer

The most frequent observation in a data set.

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

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