Question

Find the median for given data =speed:-85-100¦¦100-115¦¦115-130¦¦130-145 no.of players:-11¦¦ 9¦¦ 8¦¦ 5¦¦

Answer 1

We prepare the cumulative frequency table, as given below:

Speed(class)                        :   85-100   100-115   115-130   130-145

No. of players (f)                 :    11             9             8              5          N = 33

Cumulative frequency (cf) :    11             20          28           33

We have to find, the median of the given data.

Solution:

Here, N = 33

∴ $\dfrac{N}{2} =\dfrac{33}{2}$ = 16.5

The cumulative frequency just greater than 16.5 is 20 and the correspondence class is 100-115.

Thus, the medial class = 100-115

∴ l = 100, h = 15, f = 9, cf = 11 and $\dfrac{N}{2} =\dfrac{33}{2}$ = 16.5

Median = $l+\dfrac{(\dfrac{N}{2} -cf)}{f} \times h$

             = $100+\dfrac{(16.5 -11)}{9} \times 15$

             = $100+\dfrac{5.5}{3} \times 5$

             = 100 + 9.167

            = 109.167

Thus, the median of the given data is "equal to 109.167".

Answer 2

Given :  

  speed:-        85-100 ¦¦ 100-115  ¦¦ 115-130  ¦¦ 130-145

 no.of players:-   11    ¦¦  9            ¦¦     8         ¦¦     5      ¦¦

To Find :  Median

Solution:

                         f                 cf

85-100             11               11

100-115              9               20

115-130              8               28

130-145             5               33

Total Frequency = 33  

33/2 = 16.5

Hence Median lies  100 - 115

Median = 100   + 15 x ( 16.5 - 11) / 9

= 100 + 9.167

= 109.167

median = 109.167

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