# CLASS-10SHORT-CUT METHOD FOR FINDING MEAN OF GROUPED DATA

Short Cut Method for Finding Mean of Grouped Data (Not in Classes)

Under this method, larger quantities get converted into smaller ones, making the process of multiplication and division easier.

Method From the given data, we suitably choose a term, usually the middle term and call it the assumed mean, to be denoted by A. We find the deviations, dₐ = (xₐ - A) for each term.

∑fₐdₐ

Then we should apply the formula =>   Mean = (A + --------)

∑fₐ

Example.1)  Using short cut method, find the mean from the following data.

Variate (xₐ)   18     19     20     21     22     23     24

Frequency (fₐ)   184    212   327    376   614    372    415

Ans.) Let, the assumed mean be, A = 21

From the given data, we prepared the table given below –

Variate (xₐ)     Frequency (fₐ)    dₐ = (xₐ - A) = (xₐ - 21)        fₐdₐ

18                184                    -3                     -552

19                212                    -2                     -424

20                327                    -1                     -327

21 = A             376                     0                        0

22                614                     1                       614

23                372                     2                       744

24                415                     3                      1245

∑fₐ = 2500                                    ∑fₐdₐ = 1300

∑fₐdₐ

Mean  = (A + ---------)

∑fₐ

1300

= (21 + -------- )

2500

13

=  (21 + -------) =  21 +  0.52  =  21.52

25

Hence the mean is 21.52         (Ans.)