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Measures Of Central Tendency — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsMeasures Of Central Tendency4 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

x
f
fx
$3$
$6$
$18$
$5$
$8$
$40$
$7$
$15$
$105$
$9$
$P$
$9p$
$11$
$8$
$88$
$13$
$4$
$52$
 
$N = p + 41$
$\sum\text{fx}=\text{9p}+303$
It is given that,
Mean $= 7.68$
$\Rightarrow\frac{\sum\text{fx}}{\text{N}}=7.68$
$\Rightarrow 9p + 303p + 41 = 7.68$
$\Rightarrow 9p + 303 = 7.68p + 314.88$
$\Rightarrow 9p − 7.68p = 314.88 - 303$
$\Rightarrow 1.32p = 11.88$
$\Rightarrow p = 11.881.32 = 9$
$\Rightarrow p = 9$
$\therefore$ $P = 9$

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