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Mean And Median Workshop

Practise choosing and finding the mean and median for real data: date palms, pets, tap water, newborn babies and sumo wrestlers.

5 micro-lessons

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Choosing the Right Summary

Mean when data is balanced, median when there are outliers, and always look at the spread.

A checklist (Textbook pp. 108–113)

Sort the data or draw a dot plot.
Look for outliers.
Remember: the mean and the median always lie between the minimum and the maximum.
If there are outliers, the median is usually the better 'typical' value.

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Rintu's Date-Palm Trees

Mean, median and a dot plot for 29 tree heights.

Problem. Rintu looks after a date-palm farm in Habra. The heights of the trees (ft) are: 50, 45, 43, 52, 61, 63, 46, 55, 60, 55, 59, 56, 56, 49, 54, 65, 66, 51, 44, 58, 60, 54, 52, 57, 61, 62, 60, 60, 67. Draw a dot plot, and find the mean and median. How many trees are shorter than the average? (Textbook p. 112, Q3)

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Where Mean and Median Can Be

Both always lie between the smallest and largest value.

Where can the mean and median be?

min ≤ mean ≤ max, and min ≤ median ≤ max.

Balanced data → mean ≈ median. High outlier → mean > median. Low outlier → mean < median.

For big data sets, group repeated values to add faster.

Pets and Water

Mean, median and limits for two data sets.

Work out and describe

Figure it Out, Textbook p. 112.

Q2. Sanskruti asked her classmates how many domestic animals and pets they have. Two students were absent (—): 0, 1, 0, 4, 8, 0, 0, 2, 1, 1, 5, 3, 4, 0, 0, —, 10, 25, 2, —, 2, 4. Find the mean and median. How would you describe this data?

Q4. Daily water use from a tap (litres): 5.6, 8, 3.09, 12.9, 6.5, 12.1, 11.3, 20.5, 7.4. (a) Can the mean or median lie between 25 and 30? (b) Can the mean or median be less than the minimum, or more than the maximum?

Q2: mean, median and description*

How many values? Any outlier?

Q4: mean and median of water use*

Show the total.

Q4 (a) and (b)*

Use what the mean and median mean.

Babies, Sections and Sumo

Compare groups with mean and median.

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Newborn boys weigh 3.5, 4.1, 2.6, 3.2, 3.4, 3.8 kg. Mean and median? (Textbook p. 112, Q5)

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