Chapter 10, Problem 7MCQ

To determine

To calculate the range, median, lower quartile and upper quartile.

Answer to Problem 7MCQ

Range= 19,

Upper quartile= 31,

Lower quartile= 19,

Median= 24.

Explanation of Solution

Given information:

The data set is,

16, 19, 21, 24, 25, 31, 35

Formula used:

Range is,

  $range=\max -\min$

Median is,

  $M={\frac{n+1}{2}}^{th}$

Lower quartile is,

  $Q1=\frac{1}{4}{(n+1)}^{th}$

Upper quartile,

  $Q3=\frac{3}{4}{(n+1)}^{th}$

Calculation:

The maximum is 35.

The minimum is 16.

For range, substituting the value,

  $range=35-16$

On solving,

  $range=19$

Therefore, range is 19

For lower quartile, substituting the value,

  $Q1=\frac{1}{4}{(7+1)}^{th}$

On solving,

  $Q1=2^{nd}term$

Substituting the value,

  $Q1=19$

Therefore, lower quartile is 19.

For upper quartile, substituting the value,

  $Q3=\frac{3}{4}{(7+1)}^{th}$

On solving,

  $Q3=6^{th}term$

Substituting the value,

  $Q3=31$

Therefore, upper quartile is 31.

For median, substituting the value,

  $M={\frac{7+1}{2}}^{th}$

On solving,

  $M=4^{th}$

Substituting the values,

  $M=24$

Hence, median is 24.