Question

Calculate arithmetic mean from the data given below:
x f
0-10 5
10-20 15
20-30 20
30-40 25
40-50 20
50-60 15
60-70 5

Answer 1

Explanation:

see RS Agarwal book example

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Answer 2

Answer:

The value of arithmetic mean is 33.52

To find:

Arithmetic mean = A =?

Formula:

$x^{\prime}=\frac{\sum f_{i} y_{i}}{\sum f_{i}}$

Solution:

$\mathrm{f} \Rightarrow x_{i} \Rightarrow y_{i}=\frac{x_{i}-33.5}{10} \Rightarrow f_{i} \Rightarrow f_{i} y_{i}$

$0-10 \Rightarrow 5 \Rightarrow-2.85 \Rightarrow 5 \Rightarrow-14.25$

$10-20 \Rightarrow 15.5 \Rightarrow-1.8 \Rightarrow 15 \Rightarrow-27$

$20-30 \Rightarrow 25.5 \Rightarrow-0.8 \Rightarrow 20 \Longrightarrow-16$

$30-40 \Rightarrow 35.5 \Rightarrow 0.2 \Rightarrow 25 \Rightarrow 5$

$40-50 \Rightarrow 45.5 \Rightarrow 1.2 \Rightarrow 20 \Rightarrow 24$

$50-60 \Rightarrow 55.5 \Rightarrow 2.2 \Rightarrow 15 \Rightarrow 33$

$60-70 \Rightarrow 65.5 \Rightarrow 3.2 \Rightarrow 5 \Rightarrow 16$

$\sum f_{i}=105$

$\sum f_{i} y_{i}=20.75$

Now,

$\Rightarrow x^{\prime}=\frac{20.75}{105}$

$\therefore x^{\prime}=0.1976$

Now, the arithmetic mean is:

$\Rightarrow A=35.5+(-10 \times 0.1976)$

$\therefore A=33.52$