Question

Explain the meaning of the accompanying percentiles. (a) The 15th percentile of the head circumference of males 3 to 5 months of age in a certain city is 41.0 cm. (b) The 75th percentile of the waist circumference of females 2 years of age in a certain (c) Anthropometry involves the measurement of the human body. One goal of these measurements is to assess how body measurements may be changing over time. The following table represents the s height of males aged 20 years or older for various age groups in a certain city in 2015. Based on the percentile measurements of the different age groups, what might you conclude? Click the icon to view the data table for partc. Standing Height (cm) Age 20 - 29 30-39 40-49 50 - 59 60-69 70 - 79 80 or older 166.8 166.9 167.9 166.0 165.3 163.2 161.7 25th 171.5 171.3 172.1 170.8 170.1 167.5 166.1 Percentile 50th 176.7 176.0 176.9 176.0 175.1 172.9 170.5 75th 181.4 181.9 182.1 181.2 179.5 178.1 175.3 90th 186.8 186.2 186.0 185.4 183.7 181.7 179.4

Answer 1

A percentile indicates the value of a variable below which a given percentage of observations falls.

Example-The 30th percentile is the value of a variable such that 30% of the relevant population is below that value.

50th percentile indicates as median.

a) The 15th percentile of the head circumference of males 3 to 5 months of age in a certain city is 41.0 cm indicates that 15% of the males 3 to 5 months of age in a certain city has 41.0 cm or less head circumference.

b) The 75th percentile of the waist circumference of females 2 years of age in a certain city is 52.7cm indicates that 75% of the observations collected for 2 years of female in a certain city has waist circumference 52.7cm or less.

c) Given table is data of height of males in 2015 in a certain city.

The 10th percentile of height of males of age 20-29 is 166.8 means 10% of the males of age group 20-29 has height 166.8cm or less, 25th percentile of height of males of age 20-29 is 171.5 means 25% of the males of age group 20-29 has height 171.5cm or less, 50th percentile of height of males of age 20-29 is 176.7 means 50% of the males of age group 20-29 has height 176.7cm or less, 75th percentile of height of males of age 20-29 is 181.4 means 75% of the males of age group 20-29 has height 181.4cm or less and 90th percentile of height of males of age 20-29 is 186.8 means 90% of the males of age group 20-29 has height 186.8cm or less.

Similarly, for age group 30-39, the 10th percentile of height of males of age 30-39 is 166.9 means 10% of the males of age group 30-39 has height 166.9cm or less, 25th percentile of height of males of age 30-39 is 171.3 means 25% of the males of age group 30-39 has height 171.3cm or less, 50th percentile of height of males of age 30-39 is 176 means 50% of the males of age group 30-39 has height 176cm or less, 75th percentile of height of males of age 30-39 is 181.9 means 75% of the males of age group 30-39 has height 181.9cm or less and 90th percentile of height of males of age 30-39 is 186.2 means 90% of the males of age group 30-39 has height 186.2cm or less.

If the 10th percentile is x(say) then 10% of the relevant population has observation x or less while the remaining 90% of the relevant population has observation more than x.

If the 50th percentile is y(say) then 50% (half) of the relevant population has observation y or less while the remaining 50% of the relevant population has observation more than y.