Question

find the following measures for the data below: 9 6 19 13 4 19 7 20 11 7 0 12 12 1 10 20 16 2 7 19 6 18 15 sorted data (use commas to separate values) quartile 1 median quartile 3 interquartile range

Explanation:

Step1: Combine and sort data

0,1,2,4,6,6,7,7,7,9,10,11,12,12,13,15,16,18,19,19,19,20,20

Step2: Find position of Q1

There are $n = 23$ data - points. The position of $Q1$ is $i=\frac{n + 1}{4}=\frac{23+1}{4}=6$. So, $Q1$ is the 6th value in the sorted data, $Q1 = 6$.

Step3: Find median

The position of the median for $n = 23$ (odd - numbered data set) is $i=\frac{n + 1}{2}=\frac{23+1}{2}=12$. So, the median is the 12th value in the sorted data, Median = 11.

Step4: Find position of Q3

The position of $Q3$ is $i=\frac{3(n + 1)}{4}=\frac{3\times(23 + 1)}{4}=18$. So, $Q3$ is the 18th value in the sorted data, $Q3 = 18$.

Step5: Calculate inter - quartile range

$IQR=Q3 - Q1=18 - 6=12$

Answer:

Sorted Data: 0,1,2,4,6,6,7,7,7,9,10,11,12,12,13,15,16,18,19,19,19,20,20
Quartile 1: 6
Median: 11
Quartile 3: 18
Interquartile Range: 12