Educational worksheet for calculating statistical measures of data sets.

Let’s solve this step by step.

We are given a set of data points for “Age (years)” and “Height (inches)”. We need to find:

1. The mean of the ages
2. The median of the ages
3. The mode of the ages
4. The range of the ages

Then do the same for heights.

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Step 1: List out the Age values

From the table, the ages are:

15, 16, 17, 18, 19, 20, 21, 22, 23, 24

That’s 10 numbers.

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Step 2: Find the Mean of Ages

Mean = sum of all values ÷ number of values

Sum = 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23 + 24

Let’s add them:

15 + 24 = 39
16 + 23 = 39
17 + 22 = 39
18 + 21 = 39
19 + 20 = 39

That’s five pairs of 39 → 5 × 39 = 195

Number of values = 10

Mean = 195 ÷ 10 = 19.5

✔ Mean age = 19.5

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Step 3: Find the Median of Ages

Median is the middle value when numbers are in order.

We already have them in order:
15, 16, 17, 18, 19, 20, 21, 22, 23, 24

There are 10 numbers (even), so median is average of 5th and 6th values.

5th value = 19
6th value = 20

Median = (19 + 20) ÷ 2 = 39 ÷ 2 = 19.5

✔ Median age = 19.5

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Step 4: Find the Mode of Ages

Mode is the number that appears most often.

Looking at the list:
15, 16, 17, 18, 19, 20, 21, 22, 23, 24

Each number appears only once → no repeats.

So, there is no mode.

✔ Mode age = None (or "no mode")

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Step 5: Find the Range of Ages

Range = highest value - lowest value

Highest = 24
Lowest = 15

Range = 24 - 15 = 9

✔ Range age = 9

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Now let’s do the same for Height (inches).

Heights from the table:

65, 66, 67, 68, 69, 70, 71, 72, 73, 74

Again, 10 values.

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Step 6: Mean of Heights

Sum = 65 + 66 + 67 + 68 + 69 + 70 + 71 + 72 + 73 + 74

Pair them:

65 + 74 = 139
66 + 73 = 139
67 + 72 = 139
68 + 71 = 139
69 + 70 = 139

Five pairs of 139 → 5 × 139 = 695

Mean = 695 ÷ 10 = 69.5

✔ Mean height = 69.5

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Step 7: Median of Heights

Ordered list:
65, 66, 67, 68, 69, 70, 71, 72, 73, 74

Even number of values → average of 5th and 6th

5th = 69
6th = 70

Median = (69 + 70) ÷ 2 = 139 ÷ 2 = 69.5

✔ Median height = 69.5

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Step 8: Mode of Heights

All values appear once → no repeats.

✔ Mode height = None (or "no mode")

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Step 9: Range of Heights

Highest = 74
Lowest = 65

Range = 74 - 65 = 9

✔ Range height = 9

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Final Answer:

For Age:
- Mean: 19.5
- Median: 19.5
- Mode: No mode
- Range: 9

For Height:
- Mean: 69.5
- Median: 69.5
- Mode: No mode
- Range: 9