Question

For the data set given below, calculate the 70th percentile. (answer with an integer or decimal.) 24 45 52 78 90 120 34 67 111 10

Answer 1

The 70th percentile would be 84

Explanation:

Firstly, we order the values in ascending order

[10, 24, 34, 45, 52, 67, 78, 90, 111, 120]

Secondly, we calculate the index i

Given that the number of terms n = 10

The seventh percentile can be gotten by firstly obtaining the index i

i = (p/100) x n

where i is the index

p is the percentile = 70

n the number of terms = 10

i = (70/100) x 10

i = 7

The index number is 7

Thirdly, evaluate the 70th Percentile

The 70th can be obtained by taking the average of the 7th value in the list which is the index and the 8th value which is immediately after the index number.

[10,24,34,45,52,67,78,90,111,120]

From the list 78 and 90 are the 7th and 8th numbers respectively;

70th percentile= (78+90) /2

70th percentile = 84

Therefore the 70th percentile is 84

Answer 2

we know that

To calculate the percentile of a data set, we should first order all the values in the data set from smallest to largest.

[10,24,34,45,52,67,78,90,111,120]

As their are
10
data points

and
70% of this is
(70/100)*10=7

Take the index and the next greatest number and find the average.

Because,the index is a whole number

so

[10,24,34,45,52,67,78,90,111,120]

(78+90) /2=84

so

70th
percentile is equal to 84

the answer is

The 70th percentile is 84