Chapter 10.3, Problem 1GP

To determine

To find minimum, lower quartile, median, upper quartile and maximum.

Answer to Problem 1GP

Minimum is 35.6, Lower quartile is 35.2, Median quartile is 36.2, Upper quartile is 35.9 and Maximum is 35.6

Explanation of Solution

Given information:

Data is 36.1, 35.8, 35.2, 36.5, 36.0, 36.2, 35.7, 35.8, 35.9, 36.4, 35.6

Formula used:

Lower quartile= $\frac{(N+1)}{4}$

Medium quartile= $\frac{(N+1)}{2}$

Upper quartile= $\frac{3(N+1)}{4}$

Where, N is number of tiles

Calculation:

Sorting the data

35.2, 35.6, 35.7, 35.8, 35.8, 35.9, 36, 36.1, 36.2, 36.4, 36.5

Total data points=11

Minimum= 35.2

Maximum=36.5

For Lower quartile, substituting values,

  $=\frac{11+1}{4}$

So,

  $=\frac{12}{4}$

On solving,

  $=3^{rd}$

Substituting the value of 3^rd data point,

  $LowerQuatile=35.7$

For Medium, substituting values,

  $=\frac{11+1}{2}$

So,

  $=\frac{12}{2}$

On solving,

  $=6^{th}$

Substituting the value of $6^{th}$ data point,

  $median=35.9$

For Upper quartile, substituting values,

  $=\frac{3(11+1)}{4}$

So,

  $=\frac{3\times 12}{4}$

On solving,

  $=9^{th}$

Substituting the value of 9^th data point,

  $upperQuartile=36.2$

Hence, Minimum is 35.6, Lower quartile is 35.2, Median quartile is 36.2, Upper quartile is 35.9 and Maximum is 35.6