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State true or false.

The frequency distribution of certain data is as follows:

Class
Frequency
100-120
10
120-140
20
140-160
30
160-180
15
180-200
5

The mean of given data is 145.

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True

False

answer is B.

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Detailed Solution

The given frequency distribution table is:

Class	Frequency
100-120	10
120-140	20
140-160	30
160-180	15
180-200	5

Formula:

Mean = A + ∑ f i d i ∑ f i

where, A is the assumed mean,

f

is the frequency and d is the mean deviation of the given data.
Let us assume A=150 be the assumed mean.
The frequency distribution table will be:

Class	Frequency, $f_{i}$	Mid-value, $x_{i}$	Deviation, $d_{i}$ = $x_{i}$ -150	$f_{i} d_{i}$
100-120	10	110	-40	-400
120-140	20	130	-20	-400
140-160	30	150=A	0	0
160-180	15	170	20	300
180-200	5	190	40	200
	Σ $f_{i}$ =80			Σ $f_{i} d_{i}$ =-300

To calculate the mean, substitute the values in the formula from the above table:

A = 150, ∑ f i = 80, ∑ f i d i = 300

Applying formula:

Mean = 150 + (− 300) 80 = 150 − 3.75 = 146.25

The mean of the given data is 146.25.
Thus, the given statement is false.
So, the correct option is 2.

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