Calculate a percentile.

Question

Can you calculate a percentile but only knowing certain percentiles. Example I need to know what the 65th percentile is. I know:

25th - 5936

40th - 6862

50th - 7523

75th - 9205

90th - 11140

Answer 1

This is how Lane:

You can estimate the 65th percentile using linear interpolation between the two surrounding percentiles you already know (the 50th and 75th percentiles).

Step 1: Identify the Surrounding Percentiles

1. 50th Percentile: 7,523
2. 75th Percentile: 9,205
3. Target Percentile: 65th

Step 2: Find the Progress Between the Points

1. Distance from 50th to 75th percentile: 75 − 50 = 25 percentile points
2. Distance from 50th to 65th percentile: 65 − 50 = 15 percentile points
3. Fraction of the distance: 15 ÷ 25 = 0.60 (or 60%)

Step 3: Calculate the Estimated Value

1. Value range between 50th and 75th: 9,205 − 7,523 = 1,682
2. 60% of that range: 1,682 × 0.60 = 1,009.2
3. Add to 50th percentile value: 7,523 + 1,009.2 = 8,532.2

The estimated 65th percentile is approximately 8,532.2 (or rounded to 8,532).