Question

Find the interquartile range of the data set that consists of 10, 8, 6, 6, 5, 2, 12, 16, 10, 4.

Answer 1

interquartile range =Q3-Q1

Arrange in ascending order:

2 4 5 6 6 8 10 10 12 16

there are 10 values

Q1 = 10/4 = 2.5

the integer immediately above is equal to 3. The first quartile Q1 is at rank 3 Q1=5

Q3 =(10*3)/4 =30/4 =7.5

the integer immediately above is equal to 8 The 3rd quartile Q3 is at rank 8

Q3 = 10

interquartile range: 10-5=5

Answer 2

Okay, here are the steps to find the interquartile range of that data set:

1) Arrange the data in numerical order: 2, 4, 5, 6, 6, 8, 10, 10, 12, 16

2) Find the median (second quartile) by locating the middle number. Since there are 10 numbers, the median is the average of the 5th and 6th values, which is 8.

3) Find the first quartile (Q1) by locating the median of the lower half of the data set. The lower half is: 2, 4, 5, 6, 6. The median of this subset is 5.

4) Find the third quartile (Q3) by locating the median of the upper half of the data set. The upper half is: 8, 10, 10, 12, 16. The median of this subset is 12.

5) The interquartile range (IQR) is the difference between the third quartile and the first quartile.

So the IQR is Q3 - Q1 = 12 - 5 = 7

Therefore, the interquartile range of the given data set is 7.