Question

Saul decides to use the IQR to measure the spread of the data. Saul calculates the IQR of the data set to be . Saul asks Jasmine to check his work. Saul copies the data in numerical order from least to greatest for Jasmine.

Answer 1

The question is incomplete. The compete question is :

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?

Solution :

The inter quartile range is being measured as : 3rd quartile - 1st quartile

The 1st quartile = 25% mark

The 3rd quartile = 75% mark

The data set as given in the question is :

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

Therefore, the total number of the sample = 9

And the median is = 50

The median separates the given data sets into two equal halves-- that is the upper half and the lower half.

Let the middle of a lower half is the 1st quartile be $Q_1$

And the middle of a 2nd half is the 3rd quartile be $Q_3$

∴ $Q_1=\frac{30+50}{2}$

        $=40$

  $Q_3=\frac{56+n}{2}$

Now for the IQR of the data set to be equal to $27$,

$\frac{56+n}{2}-40=27$

$\frac{56+n}{2}=27+40$

$\frac{56+n}{2}=67$

$56 +n=134$

$n=134-56$

$n=78$