Question

# Can you please explain how can we find the 50th percentile point using this grouped frequency...

Can you please explain how can we find the 50th percentile point using this grouped frequency table? I know that it falls between scores of 56.4 % and 34.6% which corresponds to a score between 19.5 and 24.5. How can we find the exact 50th percentile point? what is the easiest way to do so? Is there a formula for that?

 INTERVALS FREQUENCIES RELATIVE FREQUENCIES CUMULATIVE FREQUENCIES CUMULATIVE PERCENTAGE 60-64 1 .01 78 100 55-59 1 .01 77 99 50-54 2 .03 76 97 45-49 2 .03 74 95 40-44 4 .05 72 92 35-39 5 .06 68 87 30-34 7 g.09 63 81 25-29 12 .15 56 72 20-24 17 .22 44 56 15-19 16 .21 27 35 10-14 8 .10 11 14 5-9 3 .04 3 4 TOTAL 78 1.0

The intervals are like

4.5 - 9.5

9.5 - 14.5

14.5 - 19.5

19.5 - 24.5

24.5 - 29.5

29.5 - 34.5

34.5 - 39.5

39.5 - 44.5

44.5 - 49.5

49.5 - 54.5

54.5 - 59.5

59.5 - 64.5

N = total number of observation = total frequency = 78

50th percentile is nothing but the median that is middlemost value of data.

50th percentile class = (50 * N ) / 100 = 39

See 39 in cumulative frequencies which covers in 44 that is class 19.5 - 24.5

50th percentile class = 19.5 - 24.5

The formula of 50th percentile is

Where l - lower limit of percentile class = 19.5

h - class size = 24.5 - 19.5 = 5

(50 * N / 100) = 39

cf = cumulative frequencg of preceeding class that is = 27

f - frequency of percentile class = 17

50th Percentile = 23.03

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