Percentiles Statistics Example 5

Follow the full solution, then compare it with the other examples linked below.

Example 5

hard
In a normally distributed data set with mean 500 and standard deviation 100, approximately what value corresponds to the 84th percentile? (Hint: use the empirical rule โ€” 84% is one standard deviation above the mean.)

Solution

  1. 1
    Step 1: By the empirical rule, approximately 68% of data falls within 1 SD of the mean. This means 34% is between the mean and +1 SD, and 50% is below the mean.
  2. 2
    Step 2: Below ฮผ+1ฯƒ\mu + 1\sigma: 50%+34%=84%50\% + 34\% = 84\%. So the 84th percentile โ‰ˆฮผ+1ฯƒ=500+100=600\approx \mu + 1\sigma = 500 + 100 = 600.

Answer

The 84th percentile is approximately 600 (one standard deviation above the mean).
In a normal distribution, the empirical rule connects standard deviations to percentiles. The 84th percentile corresponds to one standard deviation above the mean because 50% + 34% = 84% of the data lies below that point. This connection between z-scores and percentiles is fundamental in statistics.

About Percentiles

Percentiles are values that divide a ranked distribution into 100 equal parts. The nnth percentile is the value below which n%n\% of the data falls, telling you where a specific observation stands relative to the entire dataset.

Learn more about Percentiles โ†’

More Percentiles Examples

Example 1 easy

A student scored in the 85th percentile on a standardised test with 200 test-takers. What does this

Example 2 medium

Given the sorted data set of 20 values: 12, 15, 18, 20, 22, 25, 27, 30, 32, 35, 38, 40, 42, 45, 48,

Example 3 medium

In a class of 40 students, a student scored higher than 32 others. What percentile is the student at

Example 4 medium

A baby's weight is at the 25th percentile for her age group. Her parents are worried she is underwei

โ† All Percentiles Examples Percentiles Concept