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What is the position of quartile $1$ 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 quartile

1

of the scores:

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

Arrange Data Set: Arrange the data set in ascending order. $\newline$ The scores are already in ascending order: $5, 7, 11, 12, 15, 18, 19, 20, 22, 24, 28$ .
Calculate First Quartile Position: Determine the position of the first quartile. $\newline$ The position of the first quartile (Q $1$ ) is calculated using the formula: $(n + 1) / 4$ , where $n$ is the number of data points. $\newline$ For $11$ data points, $(11 + 1) / 4 = 3$ . $\newline$ So, the first quartile is at the $3^{\text{rd}}$ position.
Identify Value at Position: Identify the value at the $3^{\text{rd}}$ position. $\newline$ The value at the $3^{\text{rd}}$ position in the ordered list is $11$ . $\newline$ First quartile: $11$

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