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Data Handling II (Central Values) — Maths STD 7 — Question

Maharashtra BoardEnglish MediumSTD 7MathsData Handling II (Central Values)5 Marks
Question
Find the missing frequency (p) for the following distribution whose mean is 7.68
x:
 3
5
7
9
 11 13
f:
 6
8
15
p
 8 4
✓

Answer

Calculation of mean:
$x_i$
$f_i$
$x_if_i$
3
6
18
5
8
40
7
15
 105
9
p
 9p
11 8 88
13 4 52
Total
$\sum\text{f}_\text{i}=41+\text{p}$
$\sum\text{f}_\text{i}\text{x}_\text{i}=303+9\text{p}$
We have,
$\sum\text{f}_\text{i}=41+\text{p},\sum\text{f}_\text{i}\text{x}_\text{i}=303+9\text{p}$
$\therefore\text{Mean}=\frac{\sum\text{f}_\text{i}\text{x}_\text{i}}{\sum\text{f}_\text{i}}$
$\Rightarrow7.68=\frac{303+9\text{p}}{41+\text{p}}$
$\Rightarrow303 + 9\text{p} = 314.88 + 7.68\text{p}$
$\Rightarrow1.32\text{p} = 314.88 - 303$
$\Rightarrow\text{p}=\frac{11.88}{1.32}$
$\Rightarrow\text{p} = 9$

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