Question

Explain all three formulas of Mean of the Grouped Data.

According to class 10.
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Answer 1

Answer:

Mean Calculation for Individual Series

1. Direct Method

In this method, the formal definition of mean is used. The values of items are simply summed and divided by the number of observations.

Mean=∑X÷N

2. Assumed Mean Method

In the assumed mean method, a value is randomly selected as an assumed mean. Generally, the value is around the centre of the series as this facilitates calculations( the calculated deviations are both negative and positive around the assumed value, hence they cancel out or sum up to a very small value).

The assumed mean is found by dividing the maximum and minimum values by 2. Now deviation of each value from the assumed mean is calculated as deviation = value of the item – assumed value of mean in a separate column. The summation of these deviations are calculated and actual mean is derived using the given formula:

Mean= A + (∑d÷N)

Here, A= Assumed value of the mean

∑d= Summation of deviations and N= Number of observations

Answer 2

Question:

Explain all three formulas of Mean of the Grouped Data.

Required Answer:

According to class 10 as mentioned the mean for grouped data can be found by three methods.

$\rm (1) \underline{ Direct \: Method} :-$

$\rm \bigstar { \underline{\underline {Formula}}} \leadsto\: \boxed {\bf</p><p>\bar x = \frac{ \sum x _{i} f_{i} }{ \sum f_{i}} }$

$\rm (2) \underline{ Assumed\: \: Method} :-$

$\rm \bigstar { \underline{\underline {Formula}}} \leadsto\: \boxed{\bf</p><p>\bar x = a + \frac{ \sum f _{i} d_{i} }{ \sum f_{i}} }$

$\rm where, \: d_{i} = ( x_{i} - a)$

$\rm (3) \underline{Step \: Deviation \: Method} :-$

$\rm \bigstar { \underline{\underline {Formula}}} \leadsto\: \boxed{\bf</p><p>\bar x = a + [\frac{ \sum f _{i} u_{i} }{ \sum f_{i}} ] \times h}$

$\rm where, \: u_{i} = \frac{d _{i} }{h}$