The frequency table below shows the percentages obtained in a Biometry test for a random sample of 60 students:
Interval fi xi F
[30 – 40) 5 b1 c1
[40 – 50) 12 b2 c2
[50 – 60) 18 b3 c3
[60 – 70) 15 b4 c4
[70 – a1) 7 b5 c5
[a1 – 90) 2 b6 c6
[90 – 100) 1 b7 c7
For the percentages obtained, find the persentile.
Answers:
78
66.72
75.72
54
To find the percentile for a given percentage, we need to calculate the cumulative frequency up to that percentage and then use the formula:
Percentile = L + (N/100) * f
Where:
- L is the lower class boundary of the interval containing the percentile
- N is the total number of data points (in this case, 60)
- f is the frequency of the class interval containing the percentile
- The percentage we are looking for
First, let's calculate the cumulative frequencies for each interval:
[30-40): 5
[40-50): 5 + 12 = 17
[50-60): 17 + 18 = 35
[60-70): 35 + 15 = 50
[70-a1): 50 + 7 = 57
[a1-90): 57 + 2 = 59
[90-100): 59 + 1 = 60
Now we need to determine which interval contains the 78th percentile.
From the cumulative frequency table, we see that the 78th percentile falls between the 70th and a1th percentile intervals.
Using the formula above, we calculate the percentile as follows:
Lower boundary of interval containing 78th percentile = 70
Frequency of the interval containing the 78th percentile = 7
Percentile = 70 + (60/100) * 7 = 75.2
Therefore, the 78th percentile is 75.2.