Question 1

Which of the following best describes the purpose of a 5-number summary in statistics?

Accepted Answer

To describe the distribution of a data set using the minimum, first quartile ($$Q_1$$), median, third quartile ($$Q_3$$), and maximum.

Question 2

Given the following student ages: 19, 21, 21, 22, 22, 22, 23, 23, 24, 25, which value represents the median?

Accepted Answer

$$22$$

Question 3

If you use a TI-84 calculator to find the 5-number summary of a data set, which key sequence should you use?

Accepted Answer

STAT $$\rightarrow$$ CALC $$\rightarrow 1-$$Var Stats

Question 4

A company records the monthly salaries (in dollars) of 10 employees as follows: 4100, 2995, 2890, 4000, 3700, 4200, 3400, 3450, 3900, 3995. What is the minimum salary?

Accepted Answer

$$2890$$

Question 5

Which value in a 5-number summary is most useful for identifying the center of a data set?

Accepted Answer

Median

Question 6

Given the following 5-number summary for a data set: $$2890$$, $$3400$$, $$3900$$, $$4100$$, $$4200$$, what is the interquartile range (IQR)?

Accepted Answer

$$700$$

Question 7

If the 5-number summary of a data set is $$10$$, $$15$$, $$20$$, $$25$$, $$30$$, which value represents the third quartile ($$Q_3$$)?

Accepted Answer

$$25$$

Question 8

A boxplot is constructed using the 5-number summary. Which part of the boxplot corresponds to the interquartile range (IQR)?

Accepted Answer

The length of the box between $$Q_1$$ and $$Q_3$$

Question 9

If a data set has a 5-number summary of $$5$$, $$10$$, $$15$$, $$20$$, $$25$$, what is the range of the data?

Accepted Answer

$$20$$

Question 10

Suppose you are analyzing the monthly salaries of employees and notice that the maximum value is much higher than the third quartile ($$Q_3). $$What does this suggest about the distribution?

Accepted Answer

The data is right-skewed, indicating possible outliers at the high end.

Question 11

Which of the following is NOT included in a 5-number summary?

Accepted Answer

Mean

Question 12

If the median salary in a company is $$3900$$, and the first quartile ($$Q_1) is$$ $$3400$$, what percentage of employees earn less than $$3900$$?

Accepted Answer

50%

Question 13

A data set has the following 5-number summary: $$100$$, $$150$$, $$200$$, $$250$$, $$300. $$What is the value of $$Q_1$$?

Accepted Answer

$$150$$

Question 14

Which step is necessary before using a graphing calculator to find the 5-number summary of a data set?

Accepted Answer

Enter the data into a list (e.g., $$L_1)$$

Question 15

If the minimum value in a data set is $$2890$$ and the maximum is $$4200$$, what is the range?

Accepted Answer

$$1310$$

Question 16

A company wants to identify outliers in employee salaries. Which part of the 5-number summary is most useful for this purpose?

Accepted Answer

The minimum and maximum values

Question 17

If the interquartile range (IQR) is $$700$$ and $$Q_1 = 3400$, what is Q_3$?

Accepted Answer

$$4100$$

Question 18

Which of the following statements is TRUE about the 5-number summary?

Accepted Answer

It provides a concise summary of the spread and center of a data set.

Question 19

A data set has a minimum of $$10$$, $$Q_1 of$$ $$15$$, median of $$20$$, $$Q_3 of$$ $$25$$, and maximum of $$30. $$What is the value of the median?

Accepted Answer

$$20$$

Question 20

If you are given the 5-number summary of a data set, which additional calculation can you perform to assess the spread of the middle 50% of the data?

Accepted Answer

Calculate the interquartile range (IQR) using $$IQR = Q_3$ - Q_1$

Describing Data Numerically: 5-Number Summary and Calculator Use

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