STEP 1: Find the median of the 8 terms given.

Since the median is an even number, we take the mean of the 4th and the 5th terms in the data set given.

Median = \frac{55+60}{2} = \frac{115}{2} = 57.5

STEP 2: Find Q_{1}

Write the median in the data set given

10, 18, 34, 55, 57.5, 70, 77, 83 ,163

Now find the median of the lower terms 10 18 34 55

The median is the mean of the 2nd term and the 3rd term which is

\frac{18+34}{2} = 26.

So, Q_{1}= 26

STEP 3: Find Q_{3}

Write the median of the higher terms 70 77 83 163

The median is the mean of the 2nd term and the 3rd term which is

\frac{77+83}{2} = 80

Q_{3} = 80

STEP 4: Find the inter quartile range

IQR = 80 - 26 = 54

Skills to recall:

What is the median in statistics

https://www.mathgoodies.com/lessons/vol8/median

What is the mean in statistics

https://www.purplemath.com/modules/meanmode.htm