Chapter 12, Problem 9CT

To determine

To find the minimum, first quartile, median, third quartile and maximum of given data set and then make a box-and-whisker plot of given data set.

Answer to Problem 9CT

Minimum: $13$ ,Maximum: $61$ ,median is $32.5$ ., $Q_1=22$ and $Q_3=41$ .

Explanation of Solution

Given:

The given data set is $41,19,31,13,48,22,61,30,34,37$ .

Calculation:

Step 1:

Arrange the data in increasing order -

  

Step 2: Find the minimum and maximum: Minimum: The least number in data set is called the minimum. Therefore the minimum of the data set is $13$

Minimum: $13$

Maximum: The greatest number in data set is called maximum. Therefore the maximum of the data set is $61$ .

Maximum: $61$

Step 3: Find the median.

Median: The median is the middle value in the data set, when data values are arranged in order and it is represented by $Q_2$ . It is the average of two middle elements if the number of data sets are even.

Here the median is $\frac{31+34}{2}=32.5$ .

Step 4: Finding the first quartile and the third quartile- The first quartile is the median of the lower half of the data set when arranged in ascending order.

Therefore, the first quartile is $Q_1=22$

Similarly, thethird quartile is the median of the upper half of the data set when arranged in ascending order.

Therefore, the third quartile is $Q_3=41$

Step 5: Make a box-and-whisker plot for the data set-

A box-and-whisker plot is a graph that represents a set of data along a horizontal line. It consist three parts: a box, extended from first quartile to third quartile and has vertical line through median and two whiskers, the left whisker is extended from minimum to first quartile and the right whisker extended from third quartile to the maximum.

Box-and-Whisker plot