Question

The production of soyabean per acre, in quintal obtained by 30 farmers in Rajapur is given below.
9, 7.5, 8, 6, 5.5, 7.5, 5, 8, 5, 6.5, 5, 5.5, 4, 4, 8, 6, 8, 7.5, 6, 9, 5.5, 7.5, 8, 5, 6.5, 5, 9, 5.5, 4, 8.
From the given data, prepare a frequency table and find the average production per acre of
soyabean.

Answer 1

Answer: Average of the given data is 6.5.

Given: 9, 7.5, 8, 6, 5.5, 7.5, 5, 8, 5, 6.5, 5, 5.5, 4, 4, 8, 6, 8, 7.5, 6, 9, 5.5, 7.5, 8, 5, 6.5, 5, 9, 5.5, 4, 8.

To Find: Find the average production.

Step-by-step explanation:

Step 1: Average of a given data is ratio of sum of given data to number of data.

The given data is

9 7.5 8 6 5.5 7.5 5 8 5 6.5 5 5.5 4 4 8 6 8 7.5 6 9 5.5 7.5 8 5 6.5 5 9 5.5 4 8

After rearranging the given data we get,

4 4 4 5 5 5 5 5 5.5 5.5 5.5 5.5 6 6 6 6.5 6.5 7.5 7.5 7.5 7.5 8 8 8 8 8 8 9 9   9

Step 2:

Number(x)     - 4   5   5.5   6   6.5   7.5    8    9

Frequency(F)  -3    5    4     3    2       4     6    3 $\implies \Sigma F = 30$

Fx                   - 12  25  22   18   13    30   48   27 $\implies \Sigma Fx = 195$

Average

$=\frac{\Sigma Fx}{\Sigma F}\\\\=\frac{195}{30} \\\\=6.5$

Hence, average of the given data is 6.5.

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