Question

If the median of the following frequency distribution is 28.5 find the missing frequencies:
class interval: 0-10 10-20 20-30 30-40 40-50 50-60 Total
Total Frequency: 5 f₁ 20 15 f₂ 5 60

Answer 1

The missing frequencies are $f_{1}=8$ and $f_{2}=7$

Explanation:

Given that the median of the frequency distribution is 28.5

We need to determine the missing frequencies $f_1$ and $f_2$

Now, we shall find the cumulative frequency from the given table.

Class interval      Frequency        Cumulative frequency

       0-10                      5                                 5

      10-20                     f₁                                5+f₁

      20-30                   20                              25+ f₁

      30-40                    15                              40+ f₁

      40-50                     f₂                            40+ f₁+ f₂

      50-60                     5                            45+ f₁+ f₂

The total frequency is $N=60$

From the table we have,

$45+f_{1}+f_{2}=60$

       $f_{1}+f_{2}=15$ ------------(1)

Since, the median 28.5 lies in the interval 20-30

Therefore, Median class = 20-30

The median can be determined using the formula,

$\text {Median}=l+\frac{\frac{N}{2}-c f}{f} \times h$

Where $l=20$ , $c f=5+f_{1}$ , $\frac{N}{2}=30$ , $f=20$ and $h=30-20=10$

Substituting the above values in the formula, we get,

$28.5=20+\frac{30-\left(5+f_{1}\right)}{20} \times 10$

Simplifying, we have,

$8.5=\frac{25+f_{1}}{2}$

$17=25-f_{1}$

$f_{1}=8$

Substituting $f_{1}=8$ in equation (1), we get,

$8+f_{2}=15$

      $f_{2}=7$

Thus, the values of $f_1$ and $f_2$ are 8 and 7 respectively.

Learn more:

(1) If the median of the following frequency distribution is 28.5 find the missing frequencies:

Class interval:

0−10

10−20

20−30

30−40

40−50

50−60

Total

Frequency:

5

f1

20

15

f2

5

60

brainly.in/question/7668516

(2) The median class of a frequency distribution is 125-145. The frequency of the median class and cumulative frequency of the class preceding to the median class are 20 and 22 respectively. Find the sum of frequencies if the median is 137

brainly.in/question/13184075