Question

15. Size
5
6
7
8
9
Frequency 4. 6. 12
р
8
the mean of the above data is 7.3 find the missing value 'p'.​

Answer 1

Solution:

$\begin{array}{| c | c | c |}\cline{1-3} \bf x_{i}& \bf f_{i}& \bf f_{i}x_{i}\\ \cline{1-3} 5 & 4 & 20 \\ \cline{1-3} 6 & 6 & 36 \\ \cline{1-3} 7 & 12 & 84 \\ \cline{1-3} 8 &p& 8p \\ \cline{1-3} 9 &\sf 8& 72\\ \cline{1-3}\end{array}$

For finding mean:

$\\\\\sf{Mean = \dfrac{Sum \: of \: f_{i}x_{i}}{Sum \: of \: f_{i}}}$

$\Rightarrow \sf{7.3 = \dfrac{20+36+84+8p+72}{30+p}}$

$\Rightarrow \sf{Mean = \dfrac{212 + 8p}{30 + p}}$

$\Rightarrow \sf{7.3 = \dfrac{212 + 8p}{30 + p}}$

$\Rightarrow \sf{7.3(30+p)=212 + 8p}$

$\Rightarrow \sf{219+7.3p=212+8p}$

$\Rightarrow \sf{219-212=8p-7.3p}$

$\Rightarrow \sf{0.7p=7}$

$\Rightarrow \sf{p = \dfrac{7}{0.7}}\\\\\\\therefore \boxed{\bf{p=10}}$

Know more:

Mean for grouped data can be given by the formula Sum of all terms divided by number of terms.

There are 3 methods for finding mean of grouped data:

• Direct Mean method (as done here)
• Step deviation method
• Assumed mean method