Saul decides to use the IQR to measure the spread of data. Saul calculates the IQR of the data set to be 27. Saul asks Jasmine to check his work. Saul copies the data in numerical order from least to greatest for Jasmine. 25, 30, 50, 50, 50, 50, 56, n, 250. What is the value of n that will make the IQR of the data set equal to 27?

Step-by-step explanation:

The inter quartile range is expressed as

Third quartile - first quartile

First quartile is the 25% mark

Third quartile is the 75% mark

The given set of data is expressed as

25, 30, 50, 50, 50, 50, 56, n, 250

total number of sample = 9

Median = 50

The median separates the data into two equal halves, the lower and the upper halve.

The middle of the lower halve is the first quartile, Q1

The middle of the second halve is the third quartile, Q3

Therefore,

Q1 = (30 + 50) / 2 = 40

Q3 = (56 + n) / 2

For the IQR of the data set to be equal to 27, it means that

(56 + n) / 2 - 40 = 27

(56 + n) / 2 = 27 + 40 = 67

56 + n = 2 * 67 = 134

n = 134 - 56

n = 78