Question

7. Find the median for the following frequency distribution table:
Class 110-119 120-129 130-139 140-149 150-159 160-169
Intervals
Frequency
6 8 15
10 6 5
8. Find the median for the following frequency distribution table:
Class-interval 0-5 5-10 10 - 15 15 - 20 20 - 25 25 - 30
Frequency 5 3 9
10 8 5
​

Answer 1

(7) The median = 136.83

(8) The median = 16.5

Explanation:

(7) The sum of the frequencies = $6+8+15+10+6+5=50$

Hence, $\frac{n}{2}=25$

Let us determine the cumulative frequency:

Class interval        Frequency         Cf

109.5 - 119.5                  6                   6

119.5- 129.5                    8                  14

129.5 - 139.5                 15                  29

139.5 - 149.5                  10                 39

149.5 - 159.5                   6                  45

159.5- 169.5                    5                  50

The value $\frac{n}{2}=25$ lies close to the interval 129.5 - 139.5

Thus, $l=129.5$ , $c f=14$ , $f=15$  and $h=10$

Substituting these values in the formula, we get,

$Median =l+\left(\frac{{\frac{n}{2} -c f}}{f}\right) h$

            $= 129.5+\left(\frac{25-14}{15}\right) 10$

            $=129.5+\frac{22}{3}$

            $=129.5+7.33$

            $=136.83$

Thus, the median = 136.83

(8) The sum of the frequencies = $5+3+9+10+8+5=40$

Hence, $\frac{n}{2}=20$

Let us determine the cumulative frequency:

Class interval        Frequency         Cf

0 - 5                               5                   5

5 - 10                              3                   8

10 - 15                             9                  17

15 - 20                           10                 27

20 - 25                            8                 35

25 - 30                            5                 40

The value $\frac{n}{2}=20$ lies close to the interval 15 - 20

Thus, $l=15$ , $C f=17$ , $f=10$ and $h=5$

Substituting these values in the formula, we get,

$Median =l+\left(\frac{{\frac{n}{2} -c f}}{f}\right) h$

            $=15+\left(\frac{20-17}{10}\right) 5$

            $=15+\frac{3}{2}$

            $=15+1.5$

            $=16.5$

Thus, the median = 16.5

Learn more:

(1) brainly.in/question/7472268

(2) brainly.in/question/7472270