Question

Saul decides to use the IQR to measure the spread of the data. Saul calculates the IQR of the data set to be 27

Saul asks Jasmine to check his work. Saul coples 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

Answer 1

n = 78

Explanation:

IQR is the interquartile range of the data set.

So Saul had already arranged the data in order, that is the first step when calculating the interquartile range.

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

Next, is to find the median so we could easily separate the data into quartiles.

The median of the data 25, 30, 50, 50, 50, 50, 56, n., 250 = 50

Then, arrange the data into the first quartile and the third quartile

first quartile = 25, 30, 50, 50

third quartile = 50, 56, n., 250

first quartile median = 30 + 50 = 80/2 = 40

third quartile = 56 + n /2

The interquartile range formula is the first quartile subtracted from the third quartile:

IQR = Q3 – Q1.

Since 27 is the interquartile range, n=

27 = (56 + n /2) - 40

Use 2 to multiply through to eliminate the denominator

54 = (56 + n) - 80

n = 78