Calculate and interpret the mean as an average of a data set
The mean is one kind of average. To find it, add up every value in a data set. Then divide that total by how many values there are.
Five pumpkins go on the market scale: 2 kg, 3 kg, 4 kg, 4 kg, and 5 kg. Add them: 2+3+4+4+5=18. Divide by the 5 pumpkins. 5 goes into 18 three times with 3 left over. Keep going: add a decimal point and a zero, and 30 tenths ÷ 5 = 6 tenths. So 18÷5=3.6, and the mean mass is 3.6 kg. No pumpkin on that scale weighs 3.6 kg. The mean is one fair number for all five together.
The mean is the total shared evenly between all the values. It can differ from every value in the set. Multiplying the mean by the count gives the total again. For another group with about the same mean, you can estimate its total by multiplying that mean by the new count. This estimate may differ from the total you find by measuring every value.
Four rounds of a game have a mean score of 6. Three of the rounds scored 5, 8, and 3. First find the total: 6×4=24. Then subtract the known scores: 24-5-8-3=8. The missing round scored 8.
Count every entry when finding a mean. Repeated values each count, and a zero counts too. Divide the total by the number of entries, not by the number of gaps between them or the number of different values. After dividing, multiply the mean by the count to check that you get the total back.
To find a missing score, multiply the mean by the number of scores to get the total. Add the known scores, then subtract their sum from the total. The mean can be a decimal: to find 3.5 × 4, use 3 × 4 = 12 and four halves = 2, so the total is 14.
Mean equals the total of all values divided by how many values there are.
Practice text and two readings written for the os-taxonomy project. The rewritten reading was written for this dataset. One reading identifies the OER Commons resource Understanding Mean, Median, and Mode. Videos by Khan Academy, embedded from YouTube.
You have found a mean by sharing a total evenly. At Meadow Lane, a barrow holds five pumpkins, and the stall poster needs one number to describe their masses.
The five pumpkins weigh 2 kg, 3 kg, 4 kg, 4 kg and 5 kg. Which way gives one fair number for all five?
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