Q: Given the data set: 10, 15, 20, 25, 30, what is the range?

$$\text{Range} = 30 - 10 = 20$$

Q: If a data set has a mean of 100 and a standard deviation of 15, what is the value at the 75th percentile assuming a normal distribution?

$$100 + 0.674 \times 15 = 110.11$$

Q: A researcher finds that the heights of students are normally distributed with a mean of 170 cm and a standard deviation of 8 cm. What height corresponds to a z-score of -1?

$$170 + (-1) \times 8 = 162 cm$$

Question 1

Which of the following best describes the median in a data set?

Accepted Answer

The middle value when the data is ordered from least to greatest.

Question 2

Given the data set: 10, 15, 20, 25, 30, what is the range?

Accepted Answer

$$	ext{Range} = 30 - 10 = 20$$

Question 3

Which formula correctly calculates the sample standard deviation?

Accepted Answer

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

Question 4

A pharmaceutical company measures the weights of pills and finds the mean is 500 mg with a standard deviation of 10 mg. According to the Empirical Rule, what percentage of pills should weigh between 490 mg and 510 mg?

Accepted Answer

About 68%

Question 5

If a student scores at the 90th percentile on an exam, which statement is true?

Accepted Answer

The student scored higher than 90% of the students.

Question 6

Which of the following is NOT a measure of central tendency?

Accepted Answer

Range

Question 7

A data set has values: 2, 4, 4, 4, 5, 6, 8. What is the mode?

Accepted Answer

4

Question 8

Which formula is used to calculate the z-score for a value $$x$$?

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

Which statement about the Empirical Rule is correct?

Accepted Answer

About 68% of data falls within one standard deviation of the mean.

Question 11

A hospital records the number of patients admitted each day for a month. Which measure would best describe the most typical number of admissions?

Accepted Answer

Mode

Question 12

Which formula is used to calculate the variance for a sample?

Accepted Answer

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

Question 13

If a data set has a mean of 100 and a standard deviation of 15, what is the value at the 75th percentile assuming a normal distribution?

Accepted Answer

$$100 + 0.674 	imes 15 = 110.11$$

Question 14

Which of the following is a correct interpretation of the 25th percentile?

Accepted Answer

25% of the data falls below this value.

Question 15

A researcher finds that the heights of students are normally distributed with a mean of 170 cm and a standard deviation of 8 cm. What height corresponds to a z-score of -1?

Accepted Answer

$$170 + (-1) 	imes 8 = 162 cm$$

Question 16

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

Accepted Answer

Mean

Question 17

A teacher calculates the mean test score as 80, the median as 75, and the mode as 70. What does this suggest about the distribution of scores?

Accepted Answer

The distribution is skewed right.

Question 18

Which of the following is the correct formula for the median position in a data set with $$n$$ values?

Accepted Answer

$$\frac{n+1}{2}$$

Question 19

If the smallest value in a data set is 12 and the largest is 48, what is the range?

Accepted Answer

$$48 - 12 = 36$$

Chapter 3: Numerically Summarizing Data – Study Guide

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