Question

according to the world health organization (who), body mass index (bmi) is a statistic that indicates the ratio of a persons weight to their body volume. the centers for disease control (cdc) uses the table below to classify children from ages 2. because bmi values change as children grow, the cdc uses percentiles rather than fixed values for bmi. percentiles provide a basis of comparison for bmi over time.
weight status\tpercentile range
underweight\tless than the 5th percentile
healthy weight\t5th percentile to less than the 85th percentile
overweight\t85th to less than the 95th percentile
obese\tequal to or greater than the 95th percentile
based on data from who, a representative sample of 15 - year - old females could consist of the following 15 values.
18.3, 18.8, 15.7, 17.8, 22.6, 17.0, 21.4, 19.7, 21.9, 23.6, 19.3, 20.8, 20.2, 32.1, 25.3
using this data, calculate the 85th percentile. (round to 1 decimal place.)

Explanation:

Step1: Sort the data

$15.7, 17.0, 17.8, 18.3, 18.8, 19.3, 19.7, 20.2, 20.8, 21.4, 21.9, 22.6, 23.6, 25.3, 32.1$

Step2: Calculate the index

The formula to find the index $i$ for the $p$ - th percentile is $i=\frac{p}{100}\times n$, where $p = 85$ and $n=15$. So $i=\frac{85}{100}\times15=12.75$.

Step3: Interpolate

Since $i$ is not an integer, we use interpolation. The $12$ - th value is $23.6$ and the $13$ - th value is $25.3$. The fractional part of $i$ is $0.75$. The $85$th percentile is $23.6+(25.3 - 23.6)\times0.75=23.6 + 1.275=24.9$.

Answer:

$24.9$