Question

question 7 (2 points)
5 - number summary
select all that apply.
which of the following are true?
□ a the lower quartile separates the lower 25% of data values.
□ b the standard deviation is represented by the length of the box.
□ c the mean is inside the box.
□ d the whiskers extend from the quartiles to the most extreme values (minimum and maximum)
□ e the length of the box represents the iqr
□ f the median is inside the box.

Explanation:

Step1: Analyze option a

By definition, the lower quartile (\(Q_1\)) divides the data - set such that 25% of the data lies below it. So, the statement "The lower quartile separates the lower 25% of data values" is True.

Step2: Analyze option b

The length of the box in a box - and - whisker plot represents the inter - quartile range (\(IQR=Q_3 - Q_1\)), not the standard deviation. So, the statement "The standard deviation is represented by the length of the box" is False.

Step3: Analyze option c

In a box - and - whisker plot, the box contains the median. There is no guarantee that the mean is inside the box. For example, in a skewed distribution, the mean can be outside the box. So, the statement "The mean is inside the box" is False.

Step4: Analyze option d

In a box - and - whisker plot, the whiskers extend from \(Q_1\) to the minimum value and from \(Q_3\) to the maximum value. So, the statement "The whiskers extend from the quartiles to the most extreme values (minimum and maximum)" is True.

Step5: Analyze option e

The inter - quartile range (\(IQR\)) is calculated as \(IQR = Q_3-Q_1\), and the length of the box in a box - and - whisker plot is \(Q_3 - Q_1\). So, the statement "The length of the box represents the IQR" is True.

Step6: Analyze option f

By the construction of a box - and - whisker plot, the box is defined from \(Q_1\) to \(Q_3\), and the median (\(Q_2\)) is drawn as a line inside the box. So, the statement "The median is inside the box" is True.

Answer:

a. The lower quartile separates the lower 25% of data values.
d. The whiskers extend from the quartiles to the most extreme values (minimum and maximum).
e. The length of the box represents the IQR.
f. The median is inside the box.