Question

Calculate the interquartile range of given data
15,26,29,33,36,37,41

Answer 1

Answer:

The Interquartile range of the given data is 11

Step-by-step explanation:

To find the interquartile range, we first arrange the numbers in order.

For the given data the data is already in ascending order.

Then we will find the median of the given data.

As there are odd number of terms, the median will be the middle term, that is 33.

Now the given data is divided in two ranges -

(i) data less than the median.

(ii) data more than the median.

We know that Interquartile range = Q₃ - Q₁

where, Q₃ is the median of the upper half of the data

and Q₁ is the median of the lower half of the data

Therefore, Q₃ = 37

and Q₁ = 26

As Interquartile range = Q₃ - Q₁

=> Interquartile range = 37 - 26

                                    = 11

Therefore, the Interquartile range of the given data is 11

Answer 2

11

Given:

15, 26, 29, 33, 36, 37, 41

To calculate:

Inter-quartile range

Formula:

IQR= $Q_{3}$ - $Q_{1}$

Where,

IQR - Inter-quartile range

$Q_{3}$  - 3rd quartile

$Q_{1}$  - 1st quartile

Formula to find $Q_{1}$,

$Q_{1}$ = ($\frac{n+1}{4}$) th item

Fomula to find $Q_{3}$

$Q_{3}$ = $\frac{3(n+1)}{4}$ th item

n= 7  

$Q_{1}$= $\frac{7+1}{4}$

   = $\frac{8}{4}$

   = 2nd item

2nd item is 26  

$Q_{3}$= $\frac{3(7+1)}{4}$

    = $\frac{3*8}{4}$

    = $\frac{24}{4}$

    = 6th item

6th item is 37

IQR = 37-26 =11

The Inter-quartile range is 11.