Comprehensive review worksheet helping students practice identifying and calculating mean, median, and mode through various scenarios.

Let’s go through each question one by one. I’ll explain clearly and simply, then give you the final answers at the end.

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Question 1: Explain how to determine if you should use mean or median.

Think about your data:
- If the numbers are pretty close together and there are no super high or super low values (called “outliers”), use the mean — it’s the average.
- If there are outliers (like one really big or small number that doesn’t fit), use the median — it’s the middle number when you line them up. The median isn’t pulled around by extreme values.

Example:
Data set A: 5, 6, 7, 8, 9 → Mean = 7, Median = 7 → Either works fine.
Data set B: 5, 6, 7, 8, 100 → Mean = 25.2 (too high because of 100!), Median = 7 → Better to use median here.

So: Use mean for normal, balanced data. Use median if there are weird extremes.

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Question 2: True or False: A data set can have more than one mode.

True! Mode is just the number(s) that appear most often.

Example:
Data: 2, 3, 3, 4, 4, 5 → Both 3 and 4 appear twice → Two modes → Called “bimodal”.

You can even have three modes (“trimodal”) or more!

✔ Answer: True

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**Question 3: Would mean, median, or mode be most appropriate for this data set:
373, 346, 387, 105, 397, 299, 357, 343, 368**

Look at the numbers. Most are in the 300s… but wait — there’s a 105. That’s way lower than the rest. It’s an outlier.

If we use the mean, that 105 will pull the average down too much.

Median is better here — it ignores the outlier and gives us the true center.

Mode? All numbers are different → No mode → Not useful.

✔ So: Use median

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Question 4: Gina put numbers in order from least to greatest. Then she found the number that occurred the most frequently. Which measure did she find?

She looked for the number that shows up the most → That’s the definition of mode.

✔ Answer: Mode

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Question 5: Manuel surveyed classmates about favorite pet: cat, dog, cat, rabbit, guinea pig, dog, fish, turtle, cat. Which measure should he use?

This is categorical data — words, not numbers. You can’t add “cat + dog” or find a middle word.

The only thing that makes sense is: which pet was chosen most often?

That’s the mode.

Count:
Cat → 3 times
Dog → 2 times
Others → 1 time each

✔ So: Use mode

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**Question 6: Meteorologist recorded snowfall over 12 days:
2”, 0”, 1”, 1”, 3”, 4”, 0”, 0”, 1”, 1”, 2”, 0”**

We want to know what’s typical. Let’s look:

There are several 0s and 1s — those are common. But also a 4” day — that’s higher.

Mean might be pulled up a bit by the 4”.
Median would be the middle value — let’s sort them:

Sorted: 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 4
Middle two: 6th and 7th → both 1 → median = 1

Mode: 0 appears 4 times, 1 appears 4 times → bimodal: 0 and 1

But since there are multiple zeros and ones, and they’re low, maybe median or mode is best.

Actually — for weather data like this, where you have many zero days and some small amounts, median is usually best because it tells you the “middle” experience without being skewed by rare heavy snow days.

Also, mode could work — but since there are two modes, it’s less clear.

✔ Best choice: median

*(Note: Some might argue mode is okay too, but median is safer for numerical data with possible outliers.)*

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Question 7: True or False: A data set can have more than one mean.

False. The mean is calculated by adding all numbers and dividing by how many there are. There’s only ONE way to do that → Only ONE mean per data set.

Even if you rearrange the numbers, the sum stays the same → mean stays the same.

✔ Answer: False

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Question 8: Joanna ordered data from least to greatest. Found the two middle numbers, added them, divided by 2. What did she find?

That’s exactly how you calculate the median when you have an even number of values.

Example: Data: 2, 4, 6, 8 → Middle two: 4 and 6 → (4+6)/2 = 5 → median = 5

✔ Answer: Median

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Real Life Application: Ask 7 classmates how many siblings they have. Record answers.

Since I can’t ask real people, I’ll make up realistic data for practice.

Let’s say the answers are:
2, 1, 3, 0, 2, 4, 1

Now solve Questions 9 and 10 using this data.

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Question 9: Find the mean, median, and mode of the data set: 2, 1, 3, 0, 2, 4, 1

Step 1: Sort the data → 0, 1, 1, 2, 2, 3, 4

→ Mean: Add them up: 0+1+1+2+2+3+4 = 13
Divide by 7 → 13 ÷ 7 ≈ 1.857 (or leave as fraction: 13/7)

→ Median: Middle number → 4th number in sorted list → 2

→ Mode: Numbers that repeat → 1 appears twice, 2 appears twice → So modes are 1 and 2 (bimodal)

✔ Mean ≈ 1.86, Median = 2, Mode = 1 and 2

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Question 10: Which is more appropriate for this data set?

Siblings data is usually small whole numbers. Here, no huge outliers — max is 4, min is 0. All values are close.

Mean is fine — it’s about 1.86, which makes sense.

Median is 2 — also reasonable.

Mode has two values — so not super helpful.

In this case, since data is symmetric and no outliers, mean is perfectly fine. But median is also good.

However, for family size data, sometimes median is preferred because you can’t have half a sibling — but statistically, mean is still valid.

I’d say either mean or median is okay — but since the question asks “which is MORE appropriate”, and the data is small and clean, mean gives a precise average.

Wait — actually, let’s think again. Sibling counts are discrete (whole numbers). People don’t have 1.86 siblings. So reporting the median (2) might be more meaningful in real life.

Also, if someone had 10 siblings, it would skew the mean — but here, no problem.

Still, for categorical-like count data, median is often used.

Hmm… Actually, in surveys like this, median is commonly reported because it represents the “typical” person.

Let me check: Sorted data: 0,1,1,2,2,3,4 → half are ≤2, half ≥2 → median = 2 is solid.

Mean = 1.86 — close to 2.

But since mode is split, and mean is decimal, median feels most natural here.

✔ Final pick: median

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## ✔ FINAL ANSWERS:

1. Use mean if data is balanced; use median if there are outliers.
2. True
3. Median
4. Mode
5. Mode
6. Median
7. False
8. Median
9. Mean ≈ 1.86, Median = 2, Mode = 1 and 2
10. Median