Q: For the data set $$\{-1, 2, 3, 3, 7, 12\}$$, what is the mean?

$$\text{Mean} = \frac{-1 + 2 + 3 + 3 + 7 + 12}{6} = 4.33$$

Q: What is the median of the data set $$\{-1, 2, 3, 3, 7, 12\}$$?

$$\text{Median} = \frac{3 + 3}{2} = 3$$

Q: Given the data set $$\{-1, 2, 3, 3, 7, 12\}$$, what is the midrange?

$$\text{Midrange} = \frac{-1 + 12}{2} = 5.5$$

Q: For the data set $$\{14, 22, 17, 2, 41, 19, 22, 21, 20, 6, 11, 31, 12, 10, 7\}$$, what is the midrange?

$$\text{Midrange} = \frac{2 + 41}{2} = 21.5$$

Q: If you are asked to construct a relative frequency distribution for the number of days per week students eat dessert, what is the formula for relative frequency?

$$\text{Relative Frequency} = \frac{\text{Frequency of a class}}{\text{Total number of observations}}$$

Q: A data set has values $$\{1, 2, 3, 4, 5\}. $$What is the mean?

$$\text{Mean} = \frac{1 + 2 + 3 + 4 + 5}{5} = 3$$

Question 1

Given the data set $$x = \{7, 5, 3, -2, 9\}$$, what is the value of $$\sum x^2$?

Accepted Answer

$$\sum x^2$ = 163$$

Question 2

For the function $$f(x) = \sqrt{x}$$ and the data set $$x = \{7, 5, 3, -2, 9\}$$, what is the value of $$\sum f(x) \cdot x$$? (Assume $$\sqrt{-2} is $$not defined and exclude it from the sum.)

Accepted Answer

$$\sum f(x) \cdot x = 7 \sqrt{7} + 5 \sqrt{5} + 3 \sqrt{3} + 9 \sqrt{9}$$

Question 3

Given $$x = \{7, 5, 3, -2, 9\}$$, what is the value of $$\frac{1}{n} \sum (x - 2)^2$ where n$ is the number of data points?

Accepted Answer

$$\frac{1}{5} \left[(7-2)^2$ + (5-2)^2$ + (3-2)^2$ + (-2-2)^2$ + (9-2)^2$\right] = 29.2$$

Question 4

For the data set $$\{-1, 2, 3, 3, 7, 12\}$$, what is the mean?

Accepted Answer

$$	ext{Mean} = \frac{-1 + 2 + 3 + 3 + 7 + 12}{6} = 4.33$$

Question 5

What is the median of the data set $$\{-1, 2, 3, 3, 7, 12\}$$?

Accepted Answer

$$	ext{Median} = \frac{3 + 3}{2} = 3$$

Question 6

For the data set $$\{-1, 2, 3, 3, 7, 12\}$$, what is the mode?

Accepted Answer

$$	ext{Mode} = 3$$

Question 7

Given the data set $$\{-1, 2, 3, 3, 7, 12\}$$, what is the midrange?

Accepted Answer

$$	ext{Midrange} = \frac{-1 + 12}{2} = 5.5$$

Question 8

For the data set $$\{14, 22, 17, 2, 41, 19, 22, 21, 20, 6, 11, 31, 12, 10, 7\}$$, what is the mode?

Accepted Answer

$$	ext{Mode} = 22$$

Question 9

For the data set $$\{14, 22, 17, 2, 41, 19, 22, 21, 20, 6, 11, 31, 12, 10, 7\}$$, what is the midrange?

Accepted Answer

$$	ext{Midrange} = \frac{2 + 41}{2} = 21.5$$

Question 10

A survey asks, 'How many days per week do you eat dessert after dinner?' Which type of data is this?

Accepted Answer

Discrete quantitative

Question 11

Which measure of center is most appropriate for describing the number of days per week students eat dessert after dinner, if the data is skewed by a few students who eat dessert every day?

Accepted Answer

Median

Question 12

If you are asked to construct a relative frequency distribution for the number of days per week students eat dessert, what is the formula for relative frequency?

Accepted Answer

$$	ext{Relative Frequency} = \frac{	ext{Frequency of a class}}{	ext{Total number of observations}}$$

Question 13

Which of the following best describes a histogram for the relative frequency distribution of the number of days per week students eat dessert?

Accepted Answer

A bar graph with adjacent bars representing the frequency of each number of days

Question 14

If a data set has multiple modes, which term best describes it?

Accepted Answer

Multimodal

Question 15

A student calculates the mean number of days per week students eat dessert as $$3.2$$, but the data is heavily skewed. What is a potential issue with using the mean in this case?

Accepted Answer

The mean is sensitive to outliers and may not represent the typical value.

Question 16

Which of the following is NOT a measure of center?

Accepted Answer

Range

Question 17

If the data set is $$\{2, 4, 4, 4, 5, 6, 7\}$$, what is the mode?

Accepted Answer

$$	ext{Mode} = 4$$

Question 18

A data set has values $$\{1, 2, 3, 4, 5\}. $$What is the mean?

Accepted Answer

$$	ext{Mean} = \frac{1 + 2 + 3 + 4 + 5}{5} = 3$$

Question 19

Which of the following best describes continuous quantitative data?

Accepted Answer

Data that can take any value within a range, such as height or weight

Step-by-Step Guidance for Introductory Statistics Worksheet

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