Free Maths Calculator

Averages from a Table Calculator

Averages from a frequency table, the topic where good students suddenly divide by the wrong thing. The fx row is built in front of you, the totals are named, and the median is found by counting through the frequencies to the middle person, not the middle row.

Try It: Enter Your Numbers

Your question

Updates as you type

Answer

Method, Step by Step

    Worked Example

    A table shows goals scored: 1 goal by 3 teams, 2 by 5, 3 by 8, 4 by 4. Find the mean, median and mode.

    1. The fx row:1×3=3, 2×5=10, 3×8=24, 4×4=16
    2. Totals:Σf = 20 and Σfx = 53, so the mean is 53 ÷ 20 = 2.65
    3. Median: the middle of 20 pieces sits between the 10th and 11th, both in the "3 goals" group, so 3. Mode: 3 (frequency 8)

    Answer: Mean 2.65, median 3, mode 3

    Try These Yourself

    Values 0, 1, 2 with frequencies 4, 9, 7. What is the mode?Show answerHide answer

    Answer: 1

    The biggest frequency is 9, which belongs to the value 1.

    Σfx = 132 and Σf = 24. What is the mean?Show answerHide answer

    Answer: 5.5

    132 ÷ 24.

    Twenty pieces of data. Which positions decide the median?Show answerHide answer

    Answer: 10th and 11th

    (20 + 1) ÷ 2 = 10.5, between those two.