EZ Math

Statistics · Centre and spread

How to Find the Mean from a Frequency Table

Problem

1,2,3,4 with frequencies 2,3,4,11, 2, 3, 4 \text{ with frequencies } 2, 3, 4, 1

Answer

mean 2.4\text{mean } 2.4

A frequency table groups repeated values. Multiply each value by its frequency, add, then divide by the number of data points.

Step-by-step solution

  1. Multiply each value by its frequency.

    1(2)+2(3)+3(4)+4(1)=2+6+12+41(2) + 2(3) + 3(4) + 4(1) = 2 + 6 + 12 + 4

    Why: Each value stands for as many data points as its frequency.

  2. Add to get the total.

    2+6+12+4=242 + 6 + 12 + 4 = 24

    Why: The sum of these products is the sum of all the data values.

  3. Divide by the total frequency.

    242+3+4+1=2410=2.4\frac{24}{2 + 3 + 4 + 1} = \frac{24}{10} = 2.4

    Why: There are ten data points in total, not four.

Common mistakes

  • Dividing by the number of rows, 4, instead of the total count, 10.
  • Adding the frequencies instead of multiplying value times frequency.
  • Reporting the sum 24 and forgetting the division.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

  1. 0,1,2 with frequencies 1,2,30, 1, 2 \text{ with frequencies } 1, 2, 3

    Show answer

    mean 43\text{mean } \frac{4}{3}

  2. 2,4,6 with frequencies 3,2,12, 4, 6 \text{ with frequencies } 3, 2, 1

    Show answer

    mean 103\text{mean } \frac{10}{3}

  3. 1,2,3 with frequencies 3,1,11, 2, 3 \text{ with frequencies } 3, 1, 1

    Show answer

    mean 85\text{mean } \frac{8}{5}

  4. 5,10 with frequencies 2,35, 10 \text{ with frequencies } 2, 3

    Show answer

    mean 8\text{mean } 8

  5. 1,3,5 with frequencies 2,2,11, 3, 5 \text{ with frequencies } 2, 2, 1

    Show answer

    mean 135\text{mean } \frac{13}{5}