Question

find the percentile for the data value.

1. data set: 3 13 10 6 3 3 13 6 3 13 2 13 15 4 9 3 12 10 6 13;

data value: 6
11)
a) 40
b) 35
c) 62
d) 25

Explanation:

Step1: Arrange data in ascending order

2, 3, 3, 3, 3, 4, 6, 6, 6, 9, 10, 10, 12, 13, 13, 13, 13, 13, 15

Step2: Calculate position of percentile

The formula to find the position of the $p$ - th percentile ($L$) in a data - set of size $n$ is $L=\frac{p}{100}(n + 1)$. Here, assume we want to find the percentile for the data - value 6. First, count $n = 19$. For the data - value 6, there are 3 values of 6. The cumulative frequency of values less than 6 is 5.
The proportion of values less than 6 is $\frac{5}{19}$. To convert this to a percentile, we calculate $p=\frac{5}{19}\times100\approx 26.32$. Rounding to the nearest whole number, we can say it is approximately 25.

Answer:

D. 25