Math worksheet focusing on measures of central tendency, featuring problems on calculating mean, median, mode, and analyzing data distribution.

Let’s solve each problem step by step.

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Problem 1: Tomato plant heights — 36, 45, 52, 40, 38, 41, 50, 48

First, let’s list the numbers in order to make it easier:
→ 36, 38, 40, 41, 45, 48, 50, 52

There are 8 numbers (even count).

Range = highest - lowest = 52 - 36 = 16

Mean = add all and divide by 8
Add: 36 + 38 = 74; 74 + 40 = 114; 114 + 41 = 155; 155 + 45 = 200; 200 + 48 = 248; 248 + 50 = 298; 298 + 52 = 350
Mean = 350 ÷ 8 = 43.75

Median = average of the two middle numbers (since even count)
Middle numbers are 4th and 5th: 41 and 45
Median = (41 + 45) ÷ 2 = 86 ÷ 2 = 43

Mode(s) = number that appears most often
Looking at the list: 36, 38, 40, 41, 45, 48, 50, 52 → all appear once → no mode

✔ Final for Problem 1:
- Range: 16
- Mean: 43.75
- Median: 43
- Mode(s): none

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Problem 2: Quiz scores

Your scores: 18, 16, 19, 15, 17
Friend’s scores: 20, 20, 13, 12, 17

Let’s sort both sets:

Yours sorted: 15, 16, 17, 18, 19
Friend’s sorted: 12, 13, 17, 20, 20

a) Find mean, median, mode for both

*Your scores:*

Mean = (15+16+17+18+19) ÷ 5 = 85 ÷ 5 = 17

Median = middle number (3rd) = 17

Mode = any number repeated? All appear once → no mode

*Friend’s scores:*

Mean = (12+13+17+20+20) ÷ 5 = 82 ÷ 5 = 16.4

Median = middle number (3rd) = 17

Mode = 20 appears twice → 20

b) Who has higher mean? Higher median?

Your mean = 17, Friend’s mean = 16.4 → You have higher mean

Both medians = 17 → same median

✔ Final for Problem 2:
a) Your quiz scores: Mean=17, Median=17, Mode=none
Friend’s quiz scores: Mean=16.4, Median=17, Mode=20
b) You have the higher mean. Both have same median.

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Problem 3: When is median equal to mean? And skew direction?

We’ll do each set.

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a) Data: 2, 4, 6, 7, 8

Sorted already.

Mean = (2+4+6+7+8) ÷ 5 = 27 ÷ 5 = 5.4

Median = middle (3rd) = 6

Is mean = median? 5.4 ≠ 6 → No

Distribution: Since mean < median → data is negatively skewed (tail on left)

Wait — actually, let’s think: if mean is less than median, that usually means there are some low values pulling the mean down → negative skew.

But let’s double-check with actual shape: 2,4,6,7,8 → the lower end has smaller gaps? Actually, from 2 to 4 is +2, 4 to 6 is +2, 6 to 7 is +1, 7 to 8 is +1 → so more spread on the left? Hmm.

Actually, standard rule:
If mean < median → negatively skewed
If mean > median → positively skewed
If mean ≈ median → symmetric

Here, 5.4 < 6 → negatively skewed

✔ a) Mean=5.4, Median=6, Distribution=negatively skewed

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b) Data: 12, 18, 20, 23, 24

Sorted.

Mean = (12+18+20+23+24) ÷ 5 = 97 ÷ 5 = 19.4

Median = 3rd = 20

19.4 < 20 → mean < median → negatively skewed

Wait — but look at the numbers: 12 is quite low compared to others. Yes, pulls mean down.

✔ b) Mean=19.4, Median=20, Distribution=negatively skewed

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c) Data: 16, 17, 18, 19, 20

This is evenly spaced!

Mean = (16+17+18+19+20) ÷ 5 = 90 ÷ 5 = 18

Median = 3rd = 18

Mean = median → symmetric distribution

Not skewed.

✔ c) Mean=18, Median=18, Distribution=symmetric (not skewed)

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d) Data: 50, 60, 65, 75, 85

Sorted.

Mean = (50+60+65+75+85) ÷ 5 = 335 ÷ 5 = 67

Median = 3rd = 65

67 > 65 → mean > median → positively skewed

Why? The high values (75, 85) pull the mean up.

✔ d) Mean=67, Median=65, Distribution=positively skewed

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Now, which dataset has median = mean? Only c).

So answer to “In which dataset is the median value equal to the mean value?” → c)

And indicate normal or skewed: only c) is normal (symmetric), others are skewed as above.

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Final Answers:

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Final Answer:
1. Range: 16, Mean: 43.75, Median: 43, Mode(s): none
2. a) Your scores: Mean=17, Median=17, Mode=none; Friend’s scores: Mean=16.4, Median=17, Mode=20
b) You have the higher mean; both have the same median
3. Only dataset c) has median equal to mean.
a) Mean=5.4, Median=6, negatively skewed
b) Mean=19.4, Median=20, negatively skewed
c) Mean=18, Median=18, symmetric (normal)
d) Mean=67, Median=65, positively skewed