Question

which data set is the most spread from its mean?
26, 6, 20, 36
28, 15, 30, 15
49, 17, 4, 18
14, 20, 24, 30

Explanation:

Step1: Calculate mean for each set

• Set1: $\frac{26+6+20+36}{4} = \frac{88}{4} = 22$
• Set2: $\frac{28+15+30+15}{4} = \frac{88}{4} = 22$
• Set3: $\frac{49+17+4+18}{4} = \frac{88}{4} = 22$
• Set4: $\frac{14+20+24+30}{4} = \frac{88}{4} = 22$

Step2: Find squared deviations

• Set1: $(26-22)^2 + (6-22)^2 + (20-22)^2 + (36-22)^2 = 16 + 256 + 4 + 196 = 472$
• Set2: $(28-22)^2 + (15-22)^2 + (30-22)^2 + (15-22)^2 = 36 + 49 + 64 + 49 = 198$
• Set3: $(49-22)^2 + (17-22)^2 + (4-22)^2 + (18-22)^2 = 729 + 25 + 324 + 16 = 1094$
• Set4: $(14-22)^2 + (20-22)^2 + (24-22)^2 + (30-22)^2 = 64 + 4 + 4 + 64 = 136$

Step3: Compute variance (avg squared dev)

• Set1: $\frac{472}{4} = 118$
• Set2: $\frac{198}{4} = 49.5$
• Set3: $\frac{1094}{4} = 273.5$
• Set4: $\frac{136}{4} = 34$

Step4: Compare variances

Largest variance = 273.5 (Set3)

Answer:

49, 17, 4, 18