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
50^{th} Percentile = 23.03
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