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What is the position of the quartiles $3$ of the scores $5,7,11,12,15,18,19,20,22,24,28$

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Calculate quartiles and interquartile range

Full solution

Q. What is the position of the quartiles

3

of the scores

5,7,11,12,15,18,19,20,22,24,28

Arrange Data in Ascending Order: Arrange the data set in ascending order. $\newline$ The data set is already in ascending order: $5, 7, 11, 12, 15, 18, 19, 20, 22, 24, 28$ .
Find Median: Determine the median of the data set. $\newline$ The data set has $11$ scores, so the median is the $6$ th score, which is $18$ . $\newline$ Median: $18$
Identify Upper Half: Identify the upper half of the data set. $\newline$ The upper half includes values that are greater than $18$ . $\newline$ Upper half: $19$ , $20$ , $22$ , $24$ , $28$
Calculate Upper Half Median: Calculate the median of the upper half of the data set. $\newline$ The upper half has $5$ scores, so the median is the $3$ rd score, which is $22$ . $\newline$ Third quartile: $22$

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