Worksheet on calculating measures of center and spread for various data sets including test scores, heights, ages of senators, and sales tax rates.

Let’s solve each problem step by step. We’ll find:
→ Mode (most frequent number)
→ Median (middle number when sorted)
→ Mean (average)
→ Lower Quartile (Q1 — median of lower half)
→ Upper Quartile (Q3 — median of upper half)
→ Interquartile Range (IQR = Q3 - Q1)
→ Population Standard Deviation (σ — measure of spread for entire population)

We’ll do this for all 4 data sets.

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Problem 1: Test Scores

Data:
37, 42, 48, 51, 52, 53, 54, 54, 55
*(Note: There are 9 numbers — let me count again from the image: first row has 7, second row has 2 → total 9)*

Sorted: already sorted? Let’s list them in order to be sure:

37, 42, 48, 51, 52, 53, 54, 54, 55 ✔

Mode: Most frequent → 54 appears twice, others once → 54

Median: Middle of 9 numbers → 5th number → 52

Mean: Add all and divide by 9

Sum = 37 + 42 = 79; +48 = 127; +51 = 17