Q: Given a symmetric distribution, which of the following relationships between the mean and median is correct?

$$\text{Mean} = \text{Median}$$

Q: If a distribution is skewed left, which of the following is true?

$$\text{Mean} \u003c \text{Median}$$

Question 1

Which of the following measures of central tendency is considered resistant to extreme values in a data set?

Accepted Answer

The median

Question 2

A data set of annual incomes is highly skewed to the right due to a few extremely wealthy individuals. Which measure would best represent the 'typical' income?

Accepted Answer

The median

Question 3

Given a symmetric distribution, which of the following relationships between the mean and median is correct?

Accepted Answer

$$	ext{Mean} = 	ext{Median}$$

Question 4

Which formula correctly calculates the sample variance $$s^2$$ for a data set with $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$ and sample mean $$\overline{x}$$?

Accepted Answer

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

Question 5

A body fat dataset is summarized in a histogram that is approximately symmetric and bell-shaped. Which empirical rule can be applied to estimate the percentage of data within two standard deviations of the mean?

Accepted Answer

Approximately 95%

Question 6

Which of the following is NOT a component of the five-number summary?

Accepted Answer

The mean

Question 7

A boxplot of the ages of U.S. Presidents at inauguration shows one point far to the right of the box. What does this point represent?

Accepted Answer

An outlier

Question 8

If a distribution is skewed left, which of the following is true?

Accepted Answer

$$	ext{Mean} \u003c 	ext{Median}$$

Question 9

Which measure of dispersion is most affected by extreme values in a data set?

Accepted Answer

The standard deviation

Question 10

Suppose the ages of astronauts who walked on the moon are summarized in a boxplot. If the box is very narrow and the whiskers are short, what does this indicate about the data?

Accepted Answer

The data are tightly clustered around the median

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 dataset has a mean of 50 and a standard deviation of 5. According to the empirical rule, what is the approximate range that contains 68% of the data?

Accepted Answer

$$45 to$$ $$55$$

Question 13

Which of the following statistics is NOT resistant to outliers?

Accepted Answer

The mean

Question 14

A researcher calculates the z-score for a value in a data set. Which formula did they use?

Accepted Answer

$$z = \frac{x - \mu}{\sigma}$$

Question 15

Which scenario best illustrates the use of the five-number summary?

Accepted Answer

Summarizing the distribution of home prices in a city

Question 16

If a dataset has a mean of 100 and a standard deviation of 10, what is the z-score for a value of 120?

Accepted Answer

$$z = 2$$

Question 17

Which of the following is a correct interpretation of a boxplot with a long whisker on the right side?

Accepted Answer

The data are skewed right

Question 18

A grouped frequency table is used to summarize data. Which measure can be estimated from this table?

Accepted Answer

The estimated mean

Question 19

Which of the following best describes a resistant statistic?

Accepted Answer

A statistic that is not substantially affected by extreme values

Chapter 3: Numerically Summarizing Data – Study Notes for Statistics

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