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.
A)78
B)66.72
C)75.72
D)54
To find the percentile for a given percentage, we need to first calculate the cumulative frequency for each interval.
Cumulative frequencies:
[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 find the interval which contains the percentile we are looking for (78%):
The interval that contains the 78th percentile is [50 - 60), since 35 < 78 < 50.
Now we can use the formula for finding the percentile within an interval:
Percentile = L + [(N/100) * W]
Where:
L = Lower boundary of the interval containing the percentile (50 in this case)
N = Cumulative frequency up to the interval before the one containing the percentile (35 in this case)
W = Width of the interval (10 in this case)
Plugging in the values:
Percentile = 50 + [(35/60) * 10] = 50 + [(0.5833) * 10] = 50 + 5.8333 = 55.8333
Therefore, the 78th percentile for the percentages obtained is 55.83%.
The closest option provided is not exact, but the closest is 54%, so the answer is D) 54%.