Question 1

Which of the following best describes the information shown in the image above?

Accepted Answer

It is a visual representation of the five-number summary, showing the minimum, first quartile ($$Q_1$$), median ($$Q_2$$), third quartile ($$Q_3$$), and maximum, each dividing the data into four equal parts.

Question 2

According to the image, what percentage of the data falls between $$Q_1$$ and $$Q_3$$?

Accepted Answer

$$50\%$$

Question 3

If a data set is divided as shown in the image, what is the value at $$Q_2$$ commonly called?

Accepted Answer

The median

Question 4

Which of the following statements is true based on the image?

Accepted Answer

Each quartile boundary ($$Q_1$$, $$Q_2$$, $$Q_3) $$divides the data into four equal parts, each containing $$25\% of $$the data.

Question 5

What is the primary purpose of dividing data into quartiles as shown in the image?

Accepted Answer

To summarize the distribution of the data and identify the spread and center.

Question 6

If a value falls between $$Q_1$$ and $$Q_2 in $$the image, what can you say about its percentile rank?

Accepted Answer

It is between the 25th and 50th percentiles.

Question 7

Which of the following is NOT part of the five-number summary as depicted in the image?

Accepted Answer

The mean

Question 8

If a data set has $$Q_1 = 20$, Q_2$ = 35$$, and $$Q_3 = 50$, what is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 50 - 20 = 30$$

Question 9

Based on the image, which value divides the lower 75% of the data from the upper 25%?

Accepted Answer

$$Q_3$$

Question 10

If a data value is greater than $$Q_3 + 1.5($$IQR)$$, what does this indicate?

Accepted Answer

The value is considered an outlier.

Measures of Position and Outliers: Study Notes for Statistics Students

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