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Lesson 12

Statistics & Percentiles

Understand percentiles, quartiles, and statistical percentages.

  • master

📚 Statistics & Percentiles

Percentiles tell you what percentage of data falls below a certain value. They're used in test scores, income data, growth charts, and more.

Understanding Percentiles:

1
25th percentile (Q1): 25% of values are below this point
2
50th percentile (Median): The middle value - half above, half below
3
75th percentile (Q3): 75% of values are below this point
4
90th percentile: You're in the top 10%!
5
99th percentile: You're in the top 1%!

💡 Real-World Example

On a standardized test, if you scored at the 85th percentile, it means you performed better than 85% of test-takers.

Quartiles and IQR:

Quartiles divide data into four equal parts:

  • Q1 (25th percentile) - First quartile
  • Q2 (50th percentile) - Second quartile (median)
  • Q3 (75th percentile) - Third quartile

IQR (Interquartile Range) = Q3 - Q1

IQR represents the middle 50% of the data and is useful for identifying outliers.

Example: Income Percentiles

If the median household income is $70,000 and you earn $91,000:

1
You're above the 50th percentile (median)
2
If this is the 75th percentile, then 75% of households earn less than you
3
You're in the top 25% of earners!

Frequently Asked Questions

What is a percentile?

The percentage of values that fall below a given score. Being in the 90th percentile on a test means you scored higher than 90% of the people who took it.

What are quartiles?

The values that split a sorted data set into four equal parts: the first quartile is the 25th percentile, the median is the 50th, and the third quartile is the 75th.

Practice

Work each one out, then check yourself.

  1. In a test with scores sorted, if you scored higher than 85 out of 100 students, what percentile are you at?

    Hint: If you scored higher than 85 students, that means 85% scored below you

    Show answer

    85

  2. If the median household income is $70,000 and yours is $91,000 at the 75th percentile, what percentage of households earn less than you?

    Hint: The 75th percentile means 75% are below you

    Show answer

    75

Final Quiz

0/3

Test what you learned. Pick the correct answer for each question.

  1. A test score is in the 90th percentile. This means:

    A test score is in the 90th percentile. This means:

  2. The median is the:

    The median is the:

  3. Q3 (third quartile) corresponds to which percentile?

    Q3 (third quartile) corresponds to which percentile?