Question

complete the following statements.
in general, % of the values in a data set lie at or below the median.
% of the values in a data set lie at or below the third quartile (q3).
if a sample consists of 800 test scores, of them would be at or below the second quartile (q2).
if a sample consists of 800 test scores, of them would be at or above the first quartile (q1).
question 13
the five - number summary of a dataset was found to be

• minimum = 1
• quartile 1 = 5
• median = 11
• quartile 3 = 17
• maximum = 20

an observation will be considered an outlier if it is below.
an observation will be considered an outlier if it is above.

Explanation:

Part 1: Completing the statements about quartiles and median

First statement: Median

The median (second quartile, Q2) divides the data set into two equal parts. So, 50% of the values lie at or below the median.

Step1: Recall median definition

Median is the middle value, so 50% of data is at or below it.
$50\%$

Second statement: Third Quartile (Q3)

The third quartile (Q3) is the value where 75% of the data lies at or below it (since quartiles divide data into four equal parts, each 25%, so Q3 is after 75% of the data).

Step1: Recall quartile definition

Quartiles divide data into 4 parts (25% each). Q3 is the 75th percentile.
$75\%$

Third statement: 800 test scores, at or below Q2 (median)

Q2 (median) has 50% of data below or at it. So, 50% of 800 is calculated.

Step1: Calculate 50% of 800

$0.5 \times 800 = 400$

Step2: Result

$400$

Fourth statement: 800 test scores, at or above Q1

Answer:

Calculate $Q3 + 1.5 \times IQR$

Step1: Calculate $1.5 \times IQR$ (already 18)

Step2: Calculate upper bound

$17 + 18 = 35$

Final Answers (Part 1):

• In general, $\boldsymbol{50}\%$ of the values in a data set lie at or below the median.
• $\boldsymbol{75}\%$ of the values in a data set lie at or below the third quartile (Q3).
• If a sample consists of 800 test scores, $\boldsymbol{400}$ of them would be at or below the second quartile (Q2).
• If a sample consists of 800 test scores, $\boldsymbol{600}$ of them would be at or above the first quartile (Q1).

Final Answers (Part 2):

• An observation will be considered an outlier if it is below $\boldsymbol{-13}$.
• An observation will be considered an outlier if it is above $\boldsymbol{35}$.