Probability and statistics

Mean, median and spread

Descriptive statistics summarise a list of data with a few numbers. Order the data first; most mistakes come from skipping that step.

The rules

• Mean: sum of all values divided by their number.
• Median: the middle value of the sorted list; with an even count, the mean of the two middle values.
• Mode: the most frequent value. Range: largest minus smallest value.
• Standard deviation measures the spread around the mean: the square root of the mean squared distance.

Practice questions with solutions

Generated by the same engine as the Kollego course and solvable without a calculator. Pick an answer in your head, then open the solution.

1. 1. Find the mean of: 10, 18, 18, 10

   • a18
   • b14
   • c15
   • d13
   Show solution

   Answer: 14

   Mean = sum of values ÷ number of values.

   (10 + 18 + 18 + 10) / 4 = 56 / 4 = 14.

2. 2. Find the median of: 9, 15, 14, 10, 6, 18, 11

   • a6
   • b11
   • c12
   • d18
   Show solution

   Answer: 11

   Sort the values; the median is the middle one (for an odd count).

   Sorted: 6, 9, 10, 11, 14, 15, 18. The middle value is 11.

3. 3. Find the mean of: 9, 11, 15, 12, 16, 7, 7

   • a11
   • b10
   • c12
   • d16
   Show solution

   Answer: 11

   Mean = sum of values ÷ number of values.

   (9 + 11 + 15 + 12 + 16 + 7 + 7) / 7 = 77 / 7 = 11.

4. 4. Find the mean of: 13, 18, 16, 5

   • a14
   • b13
   • c12
   • d18
   Show solution

   Answer: 13

   Mean = sum of values ÷ number of values.

   (13 + 18 + 16 + 5) / 4 = 52 / 4 = 13.

5. 5. Find the median of: 2, 10, 4, 8, 4

   • a2
   • b5
   • c4
   • d10
   Show solution

   Answer: 4

   Sort the values; the median is the middle one (for an odd count).

   Sorted: 2, 4, 4, 8, 10. The middle value is 4.

6. 6. Find the median of: 18, 9, 7, 6, 21, 12, 8

   • a10
   • b9
   • c6
   • d21
   Show solution

   Answer: 9

   Sort the values; the median is the middle one (for an odd count).

   Sorted: 6, 7, 8, 9, 12, 18, 21. The middle value is 9.

Common mistakes

• Taking the middle of the unsorted list as the median.
• Dividing by the wrong count when computing the mean.
• Confusing range with standard deviation.

Related topics

All maths topics · T-Kurs · M-Kurs · W-Kurs