Question

class interval-50-52,53-55,56-58,59-61,62-64 frequency-15,110,135,115,25 find mode of the following data

Answer 1

make the class interval like the following:-
49.5-52.5,52.5-55.5,55.5-58.5,58.5-61.5,61.5-64.5

Maximum frequency=135
Model class=55.5-58.5

l=55.5
f1=135
f2=115
f0=110
h=3

mode = l+(f1-f0/2f1-f0-f2)×h
=55.5+(135-110/2×135-110-115)×3
=55.5+(25/270-225)×3
=55.5+(25/45)×3
=55.5+25/15
=55.5+5/3
=55.5+1.67
mode = 57.17

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Answer 2

57.1

Class interval          Frequency

  50-52                        15

  53-55                        110

  56-58                        135

  59-61                        115

  62-64                         25

Formula:

Mode = L + $\frac{\Delta_{1} }{\Delta_{1} + \Delta_{2} }$ * i

where,

L   = Lower limit of modal class

$\Delta_{1}$ = difference between the frequency of modal class and pre-modal class

$\Delta_{2}$ = difference between the frequency of modal class and post-modal class

i    = class interval

The class interval of higher frequency-135 is 56-58

L   = 56

Frequency of modal class         - 135

Frequency of pre-modal class  - 110

Frequency of post-modal class - 115

$\Delta_{1}$  = 135 - 110

      = 25

$\Delta_{2}$  = 135 - 115

      = 20

i      = 2

Substitute in the formula,

Mode = 56+( $\frac{25}{20+25}$ * 2)

          = 56+( $\frac{25}{45}$ * 2)

          = 56+ (0.55 * 2)

          = 56+ 1.1

          = 57.1

The mode of the given data is 57.1.