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Question : Find arithmetic average (mean) of the following data 4,3,3,3,4,4,4,4,6,4,3,3,3,3,5,5,5,3,3,3,3,4,3,4,3,3,4,4,4,4,4,3
Answer :
For the given data first we shall make a frequency table
| xi | frequency (fi) |
| 3 | 15 |
| 4 | 13 |
| 5 | 3 |
| 6 | 1 |
\[N=\sum_{i=1}^{32}(f_{i}= 15+13+3+1=32\]
By the formula of mean (arithmetic mean)
\[x¯ =\frac{1}{N}\sum_{i=1}^{N}(f_{i}*x_{i} ) =\frac{1}{32}\sum_{i=1}^{N}(f_{i}*x_{i} ) =\frac{3*15+4*13*5*3+6*1}{32} \]
Since
\[x¯ =\frac{1}{n}\sum_{i=1}^{}(f_{i}*x_{i} ) = \]
Therefore mean of the frequency distribution of the table is 25.968.
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