Correct Answer - Option 1 : 120
Given:
Mean of the given data is 9.5 and data along with the frequency is given
Formula Used:
Direct formula for mean \(= {\rm{\;}}\sum {{\rm{f}}_{\rm{i}}}{{\rm{x}}_{\rm{i}}}/\sum {{\rm{f}}_{\rm{i}}}\)
Where x is observation and f is frequency of observation
Calculation:
Here we need to calculate the value of \({f_i}{x_i}\) and \({f_i}\) and let the missing frequency be K
|
\({{\bf{x}}_{\bf{i}}}\)
|
\({{\bf{f}}_{\bf{i}}}\)
|
\({{\bf{f}}_{\bf{i}}}{{\bf{x}}_{\bf{i}}}\)
|
|
3
|
10
|
30
|
|
5
|
7
|
35
|
|
7
|
8
|
56
|
|
10
|
K
|
10K
|
|
11
|
12
|
132
|
|
13
|
11
|
143
|
|
|
\(\sum {{\bf{f}}_{\bf{i}}} = 48 + {\bf{K}}\)
|
\(\sum {{\bf{f}}_{\bf{i}}}{{\bf{x}}_{\bf{i}}} = 396 + 10{\bf{K}}\)
|
Now, Put these value in the given formula
∴ 9.5 = (396 + 10K)/48 + K
⇒ 456 + 9.5K = 396 + 10K
⇒ 0.5K = 60
⇒ K = 120
Hence, option (1) is correct
