Choosing the Best Average | Cazoom Maths Worksheets - Free Printable

Let's go through each question and determine the best measure of average (Mean, Median, Mode, or Range), along with a clear reason for each choice.

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

- ✔ Best measure: Mode
- 📌 Reason: The mode is the most frequently occurring value. Since we're looking for the *most popular* type of footwear (e.g., sneakers, boots, sandals), we want to know which one appears most often — that’s exactly what the mode tells us.

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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 divides the data into two equal halves. If a student's score is above the median, they are in the top half; below it, they're in the bottom half. This makes the median ideal for ranking performance.

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

- ✔ Best measure: Median
- 📌 Reason: The data set includes an outlier (98), which would heavily skew the mean. The median is less affected by extreme values and gives a better central value here.
*(Note: While you could calculate the mean, the median is more representative in this case.)*

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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 gives a single overall average that reflects the total performance of the class. Students can compare their individual scores to this average to see how they did relative to the whole group.

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

- ✔ Best measure: Mean
- 📌 Reason: Mass is a continuous numerical variable, and the mean provides a reliable central tendency when comparing groups. It allows meaningful comparisons between regions.

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

- ✔ Best measure: Mode
- 📌 Reason: Hair colour is a categorical variable (not numerical). You cannot calculate a mean or median for categories like "brown", "blonde", etc. The mode (most common hair colour) is the only appropriate measure here.

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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 know which shoe size is most commonly worn (i.e., sold). Stocking more of the mode size will meet customer demand best.

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

- ✔ Best measure: Range
- 📌 Reason: The range measures the difference between the highest and lowest values. Since the question asks about the *spread*, not the central tendency, the range is the correct choice.

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

- ✔ Best measure: Mean
- 📌 Reason: Pocket money is numerical, and unless there are extreme outliers, the mean gives a good overall average. It represents the total amount shared equally among all friends.

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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 (e.g., by phone or app), and the person with the most votes wins. That’s the mode — the most frequent outcome.

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✔ Final Summary Table:

| Question | Best Measure | Reason |
|--------|--------------|--------|
| 1 | Mode | Most common footwear |
| 2 | Median | Splits class into top/bottom half |
| 3 | Median | Outlier (98) skews the mean |
| 4 | Mean | Overall average for comparison |
| 5 | Mean | Compare continuous data across regions |
| 6 | Mode | Categorical data (hair colour) |
| 7 | Mode | Most popular shoe size |
| 8 | Range | Measures spread (difference between max and min) |
| 9 | Mean | Average of numerical amounts |
| 10 | Mode | Winner has most votes |

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