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Mean, Median and Mode of Ungrouped Data — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsMean, Median and Mode of Ungrouped Data5 Marks
Question
Find the missing frequency p for the following frequency distribution whose mean is 28.25.
x
15
20
25
30
35
40
f
8
7
p
14
15
6
✓

Answer

We prepare the follwoing frequency distribution table:
(xi)
(fi)
fixi
15
8
120
20
7
140
25
p
25p
30
14
420
35
15
525
40
6
240
 
$\sum\text{f}_\text{i}=50+\text{p}$
$\sum\text{f}_\text{i}\text{x}_\text{i}=14145+25\text{p}$
Mean $=\frac{\sum\text{f}_\text{i}\text{x}_\text{i}}{\sum\text{f}_\text{i}}=\frac{1445+25\text{p}}{50+\text{p}}=28.25$
$\therefore\ \frac{1445+25\text{p}}{50+\text{p}}=28.25$
$\Rightarrow1445+25\text{p}=(28.25)(50+\text{p})$
$\Rightarrow1445+25\text{p}=1412.50+28.25\text{p}$
$\Rightarrow-28.25\text{p}+25\text{p}=-1445+1412.50$
$\Rightarrow-3.25\text{p}=-32.5$
$\Rightarrow\text{p}=\frac{32.5}{3.25}=10$
$\therefore\ $the value of p = 10

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