Question

The weights (in pounds) of 17 preschool children are

37, 30, 47, 24, 46, 39, 36, 21, 31, 32, 27, 29, 26, 42, 20, 35, 48
Find 25th and 80th percentiles for these weights.
(a)
(b)
The 25th percentile: pounds
The 80th percentile: pounds

Answer 1

25th percentile is 27

80th percentile is 42

Explanation:

Arrange the data in ascending order. This gives
20, 21, 24, 26, 27, 29, 30, 31, 32, 35, 36, 37, 39, 42, 46, 47, 48

You want to find the 25th percentile in the data set. At least 25% of the data values will be less than this number.

The index of the sorted data set represents the position. The first number, 20 has an index of 1, the second, 21 has an index of 2, etc. To find the index of the 25th percentile, apply the formula

`i = (p)/(100) \cdot N`

where i represents the index

For 25th percentile

`i = (25)/(100) \cdot 17`

`i = 4.25`

Round it up to the next integer = 5

The data value in the 5th position is 27

20, 21, 24, 26, 27, 29, 30, 31, 32, 35, 36, 37, 39, 42, 46, 47, 48

So 25th percentile is 27

The 80th percentile index = 80/100 x 17 = 13.6

Round it up to 14

The data in the 14th position is 42

20, 21, 24, 26, 27, 29, 30, 31, 32, 35, 36, 37, 39, 42, 46, 47, 48

Therefore, the 80th percentile is: 42