Measures of Center and Variability

Mean = Sum of all values ÷ Number of values

Step 1: Add all values 8 + 12 + 15 + 10 + 5 = 50

Step 2: Count how many values 5 values

Step 3: Divide Mean = 50 ÷ 5 = 10

Answer: 10

Step 1: Put in order from least to greatest 2, 3, 4, 5, 7, 8, 9

Step 2: Find the middle value 7 values total → middle is the 4th value 2, 3, 4, [5], 7, 8, 9

Answer: Median = 5

MEAN: Sum: 6 + 8 + 8 + 10 + 12 + 8 + 14 = 66 Count: 7 values Mean = 66 ÷ 7 ≈ 9.43

MEDIAN: Ordered: 6, 8, 8, 8, 10, 12, 14 Middle value (4th): 8

MODE: Most frequent value: 8 (appears 3 times)

Answers: • Mean ≈ 9.43 • Median = 8 • Mode = 8

RANGE: Range = Max - Min = 30 - 5 = 25

IQR (Interquartile Range):

Step 1: Find median (Q2) Ordered: 5, 8, 12, 15, [18], 20, 22, 25, 30 Q2 = 18

Step 2: Find Q1 (median of lower half) Lower half: 5, 8, 12, 15 Q1 = (8 + 12)/2 = 10

Step 3: Find Q3 (median of upper half) Upper half: 20, 22, 25, 30 Q3 = (22 + 25)/2 = 23.5

Step 4: Calculate IQR IQR = Q3 - Q1 = 23.5 - 10 = 13.5

Answers: • Range = 25 • IQR = 13.5

STUDENT A: Mean = (85 + 87 + 86 + 88 + 84) ÷ 5 = 430 ÷ 5 = 86 Range = 88 - 84 = 4

STUDENT B: Mean = (70 + 90 + 80 + 95 + 75) ÷ 5 = 410 ÷ 5 = 82 Range = 95 - 70 = 25

ANALYSIS: a) Student A mean = 86, Student B mean = 82

b) Student A range = 4, Student B range = 25

c) Student A is MORE CONSISTENT because their range is much smaller (4 vs 25). Their scores are clustered close together (84-88), while Student B's scores vary widely (70-95). A smaller range means less variability and more consistency.

Answers: a) A: 86, B: 82 b) A: 4, B: 25 c) Student A is more consistent (smaller range/variability)