Willow Pratt

2022-07-05

How do you find the range and interquartile range for 37, 19, 13, 11, 10?

Kayley Jackson

Expert

Let us first arrange them in increasing order and data appears as
10, 11, 13, 19, 37
As the range is difference between maximum and nimimum
Range is 37-10=27
Median is the value of $\left(\frac{n+1}{2}{\right)}^{th}$ term i.e. $\frac{5+1}{2}={3}^{rd}$ term i.e. 13
First quartile ${Q}_{1}$ is $\left(\frac{n+1}{4}{\right)}^{th}=\left(1\frac{1}{2}{\right)}^{th}$ term and third quartile ${Q}_{3}$ is
$3\left(\frac{n+1}{4}{\right)}^{th}=\left(4\frac{1}{2}{\right)}^{th}$ term.
Hence, we can take ${Q}_{1}$ as $\frac{10+11}{2}=10\frac{1}{2}$ and ${Q}_{3}$ as $\frac{19+37}{2}=28$
As interquartile range is ${Q}_{3}-{Q}_{1}$ , it is $28-10\frac{1}{2}=17\frac{1}{2}$

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