Question

1.25, 1.64,1.91,2.31,2.37,2.38,2.84,2.87,2.93,2.94,2.98,3.00,3.09,3.22,3.41,3.55.

Use this dataset two answer the questions below.

(a) What is the percentile values of (i) 2.31 and of (ii) 3.09?

(b) Find values of 30th30th and 90th90th percentiles for the above data set, i.e., P30P30 and P90P90.

Answer 1

a)

The percentile values are obtained by following these steps,

Step 1: sort the data value smallest to largest.

rank	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
data	1.25	1.64	1.91	2.31	2.37	2.38	2.84	2.87	2.93	2.94	2.98	3	3.09	3.22	3.41	3.55

Step 2: The percentile value is obtained using the formula,

(i) 2.31

The rank for the value of 2.31 is 4.

(ii) 3.09

The rank for the value of 3.09 is 13.

b)

To calculate the percentile, follow these steps,

Step 1: sort the data value smallest to largest.

Step 2: Calculate the rank for the pth percentile using the formula,

30th percentile,

Now calculate the data value for 5.1th position,

90th percentile,

Now calculate the data value for 15.3th position,