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The mean of the following distribution is 18. Find the frequency f of the class 19-21.
| Class | 11-13 | 13-15 | 15-17 | 17-19 | 19-21 | 21-23 | 23-25 |
| Frequency | 3 | 6 | 9 | 13 | f | 5 | 4 |
Given: The mean of given table $=18$.
To do: To find the frequency f of the class $19-21$.
Solution:
| Classs | Mid-value $x_{i}$ | Frequency $( f_{i})$ | $d_{i}=x_{i}-18$ | $u_{i}=\frac{x_{i}-18}{2}$ | $f_{i}u_{i}$ |
| 11-13 | 12 | 3 | -6 | -3 | -9 |
| 13-15 | 14 | 6 | -4 | -2 | -12 |
| 15-17 | 16 | 9 | -2 | -1 | -9 |
| 17-19 | 18 | 13 | 0 | 0 | 0 |
| 19-21 | 20 | f | 2 | 1 | f |
| 21-23 | 22 | 5 | 4 | 2 | 10 |
| 23-25 | 24 | 4 | 6 | 3 | 12 |
| $\sum f_{i}=40+f$ | $\sum f_{i}u_{i}$ |
$\sum f_{i}u_{i}=f-8$
And $\sum f_{i}=40+f$
$h=2,\ A=18$
As known Mean $= A+h( \frac{\sum f_{i}u_{i}}{\sum f_{i}})$
$18=18+2( \frac{f-8}{40+f})$
$\Rightarrow ( \frac{f-8}{40+f})=0$
$\Rightarrow f-8=0$
$\Rightarrow f=8$
Hence $f=8$.
Updated on: 10-Oct-2022
2K+ Views
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