Question

Find the following measures of dispersion for the data below:18 7 16 15 342 0 0 1280157 14Sorted Data0,0,0,2,3,4,7,7,8,12,14,15,15,16,18Minimum0oQuartile 1MedianQuartile 3MaximumRange18Interquartile RangeEnter an integer or decimal number (more..]18 ✔

Answer 1

`Q1=1,Q_2=7,Q_3=15,IQR=13`

1) Let's begin by enlisting the data orderly from the least to the greatest one.

`0,0,0,2,3,4,7,7,8,12,14,15,15,16,18`

2) Quartiles

As requested, we need to find the quartiles so let's start out with the 2nd Quartile, i.e. the median.

0,0,0 2, 3,4, 7,7, 8,12,14,15,15,16,18

Note that there are 15 data points, so let's bold the middle number. The one that divides the distribution evenly:

0,0,0,2, 3,4, 7, 7, 8,12,14,15,15,16,18

So the Median or Q2 is 7

b) Quartile 1

Similarly, we can find the median of the first half:

0,0,0,2, 3,4, 7

So, the 1st Quartile is 2

c) Quartile 3

For the 3rd quartile, we can select the 2nd half and find the middle number.

8,12,14,15,15,16,18

So the 3rd Quartile is 15.

d) Interquartile Range

The IQR is found by the difference between Q3 and Q1

`Q_3-Q_1=15-2=13`