Q: Suppose the mean waist circumference of 2-year-old males is 48.5 cm with a standard deviation of 4.8 cm. According to the Empirical Rule, about 95% of 2-year-old males will have waist circumferences between what values?

$$48.5 \pm 2 \times 4.8 = 38.9 \text{ cm to } 58.1 \text{ cm}$$

Question 1

Which of the following best describes the arithmetic mean of a variable from a population?

Accepted Answer

It is computed by adding all the values of the variable in the data set and dividing by the number of observations.

Question 2

Given the data set: 23, 36, 23, 18, 5, 26, 43, what is the sample mean?

Accepted Answer

$$\frac{23+36+23+18+5+26+43}{7} = 24.857$$

Question 3

Which formula correctly represents the sample standard deviation $$s$$ for a data set $$x_1$$, $$x_2$$, ..., x_n$$ with sample mean $$\bar{x}$$?

Accepted Answer

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

Question 4

A data set is said to be skewed right if:

Accepted Answer

The mean is substantially larger than the median.

Question 5

What is the range of the data set: 23, 36, 23, 18, 5, 26, 43?

Accepted Answer

$$43 - 5 = 38$$

Question 6

If a distribution is bell-shaped, what percentage of the data falls within two standard deviations of the mean according to the Empirical Rule?

Accepted Answer

Approximately 95%

Question 7

Suppose the mean waist circumference of 2-year-old males is 48.5 cm with a standard deviation of 4.8 cm. According to the Empirical Rule, about 95% of 2-year-old males will have waist circumferences between what values?

Accepted Answer

$$48.5 \pm 2 	imes 4.8 = 38.9 	ext{ cm to } 58.1 	ext{ cm}$$

Question 8

Which of the following is the correct formula for the population variance $$\$$sigma^2$$?

Accepted Answer

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

Question 9

A z-score is used to:

Accepted Answer

Compare variables with different centers and spreads by converting them to a common scale.

Question 10

Given a data set with $$Q_1 = 18$, Q_3$ = 36$$, what is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 18$$

Question 11

Which of the following is NOT a step in checking for outliers using quartiles?

Accepted Answer

Calculate the mean of the data set.

Question 12

If a data set has the following five-number summary: 5, 18, 23, 36, 43, what is the median?

Accepted Answer

23

Question 13

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

Accepted Answer

The value that occurs most frequently in the data set.

Question 14

A boxplot is useful for:

Accepted Answer

Displaying the five-number summary and identifying outliers.

Question 15

If a data set is symmetric, which of the following is true?

Accepted Answer

Mean = Median

Question 16

Which formula is used to compute the weighted mean $$\bar{x}_w$$?

Accepted Answer

$$\bar{x}_w = \frac{\sum w_i x_i}{\sum w_i}$$

Question 17

According to Chebyshev's Inequality, at least what percentage of data lies within $$k=2$$ standard deviations of the mean for any data set?

Accepted Answer

75%

Question 18

Which of the following statements about degrees of freedom is correct?

Accepted Answer

Degrees of freedom refer to the number of values that are free to vary when computing a statistic.

Question 19

If a data set has a mean of 50 and a standard deviation of 5, what is the z-score for a value of 60?

Accepted Answer

$$z = \frac{60 - 50}{5} = 2$$

Question 20

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

Accepted Answer

Mean

Chapter 3: Numerically Summarizing Data – Measures of Central Tendency, Dispersion, and Position

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