Q: What is the formula for the midrange of a data set?

$$\text{midrange} = \frac{\text{max} + \text{min}}{2}$$

Question 1

Which of the following best describes the purpose of descriptive statistics?

Accepted Answer

To describe and summarize the main features of a data set.

Question 2

Given the following notations, which one represents the sum of a set of values?

Accepted Answer

$$\Sigma$$

Question 3

In a study of all 50 states, 10 states are selected and each state’s income per capita is recorded. What are the population size and sample size?

Accepted Answer

Population size = 50, Sample size = 10

Question 4

Which of the following is NOT a measure of center?

Accepted Answer

Variance

Question 5

What is the formula for the sample mean?

Accepted Answer

$$\bar{x} = \frac{\Sigma x}{n}$$

Question 6

Calculate the mean for the following sample: 12, 25, 38, 5, 20.

Accepted Answer

Mean = 20

Question 7

Which measure of center is most resistant to extreme values (outliers)?

Accepted Answer

Median

Question 8

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

Accepted Answer

The mean and median will be equal.

Question 9

Given the data set: 101, 106, 109, 116, 118, 135, 568, which measure of center is more appropriate and why?

Accepted Answer

The median, because it is not affected by the extreme value 568.

Question 10

Which formula is used to find the mean of grouped data?

Accepted Answer

$$\bar{x} = \frac{\Sigma (x \cdot f)}{\Sigma f}$$

Question 11

A student’s final grade is calculated using the following grades and weights: Test 1: 92 (15%), Test 2: 94 (15%), Test 3: 98 (15%), Final Exam: 87 (25%), Homework: 98 (10%), Quiz: 84 (10%), Project: 84 (5%), Attendance: 89 (5%). What type of mean should be used?

Accepted Answer

Weighted mean

Question 12

Which of the following is true about the mode?

Accepted Answer

It can be used with categorical (qualitative) data.

Question 13

What is the formula for the midrange of a data set?

Accepted Answer

$$	ext{midrange} = \frac{	ext{max} + 	ext{min}}{2}$$

Question 14

Which of the following is NOT a measure of spread?

Accepted Answer

Median

Question 15

A data set has the following values: 31, 19, 78, 65, 95. What is the midrange?

Accepted Answer

Midrange = 57

Question 16

Which of the following statements about the mean is correct?

Accepted Answer

The mean is affected by extreme values.

Question 17

If a data set is skewed to the right, which measure of center is likely to be greater?

Accepted Answer

The mean

Question 18

Which of the following best describes a bimodal data set?

Accepted Answer

A data set with two values that occur with the greatest frequency.

Question 19

Which measure of center can be used with qualitative (categorical) data?

Accepted Answer

Mode

Question 20

Which of the following is a correct interpretation of the formula $$\bar{x} = \frac{\Sigma (x \cdot w)}{\Sigma w}$$?

Accepted Answer

It is used to calculate the weighted mean.

Descriptive Statistics: Measures of Center and Spread (Chapter 3 Study Notes)

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