Question

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

Answer 1

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

50^th Percentile = 23.03