Choosing the Best Average | Cazoom Maths Worksheets - Free Printable

Here's the solution to the worksheet “Choosing the Best Average”, with explanations for each choice.

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Key Definitions:

- Mean: The arithmetic average. Add all values and divide by the number of values. Sensitive to outliers.
- Median: The middle value when data is ordered. Good for skewed data or when you want to split the group in half.
- Mode: The most frequently occurring value. Used for categorical data or to find the most common item.
- Range: The difference between the highest and lowest values. Measures spread, not central tendency.

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## Answers & Explanations

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1) To find out the most popular footwear in your class

✔ Best measure: Mode
Reason: Footwear types (e.g., sneakers, boots, sandals) are categorical data — not numbers you can average. The mode tells you which type appears most often, i.e., the *most popular*.

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2) To find the average mark in a test so that students can tell if they were in the top half or the bottom half of the class.

✔ Best measure: Median
Reason: The median splits the data into two equal halves — exactly what’s needed to determine if someone is in the top or bottom half. It’s not affected by extreme scores (like one student scoring 100 or 0).

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3) To find the average for 12, 15, 98, 22, 11, 35.

✔ Best measure: Median
Reason: The value 98 is an outlier — it’s much higher than the rest. The mean would be pulled upward and give a misleading “average”. The median (middle value when ordered) gives a better sense of the typical value.
*(Ordered: 11, 12, 15, 22, 35, 98 → Median = (15+22)/2 = 18.5)*

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4) To find the average mark in a test so that students can gauge how well they have done compared with everyone else.

✔ Best measure: Mean
Reason: The mean considers every score and gives a true “overall average” that reflects the entire class performance. Students can compare their score to this average to see if they’re above or below the class norm.

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5) To compare the average mass of new born babies born in different parts of the UK.

✔ Best measure: Mean
Reason: Mass is numerical and typically normally distributed (no extreme outliers). The mean gives the best overall comparison between regions because it uses all data points.

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6) To find the average hair colour for all students in your school.

✔ Best measure: Mode
Reason: Hair colour is categorical (blonde, brown, black, red, etc.). You can’t calculate a “mean” or “median” for colours. The mode tells you the most common hair colour.

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7) To work out how many shoe sizes to stock if you owned a shoe shop.

✔ Best measure: Mode
Reason: You want to stock the sizes that sell the most. The mode tells you the most frequently bought size(s), helping you meet customer demand.

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8) To find the spread of ages at a party.

✔ Best measure: Range
Reason: “Spread” refers to how dispersed the data is — from youngest to oldest. Range = highest age – lowest age. This directly answers the question about spread.

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9) To find the average pocket money received by all your friends.

✔ Best measure: Mean
Reason: Pocket money is numerical data. Assuming no extreme outliers (e.g., one friend gets £100 while others get £5), the mean gives a fair average amount received. If there were huge differences, median might be better — but the question implies general comparison.

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10) To choose the winner of a talent show where the viewers decide who wins.

✔ Best measure: Mode
Reason: Viewers vote for their favourite — likely choosing one person. The contestant with the most votes (mode) wins. This is literally the definition of mode: the most frequent outcome.

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## ✔ Final Answer Summary:

| Question | Best Measure |
|----------|--------------|
| 1 | Mode |
| 2 | Median |
| 3 | Median |
| 4 | Mean |
| 5 | Mean |
| 6 | Mode |
| 7 | Mode |
| 8 | Range |
| 9 | Mean |
| 10 | Mode |

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