Question

which data set has a mean of 15, a median of 14, and a mode of 11?
11, 11, 13, 15, 20
5, 11, 14, 14, 31
11, 11, 14, 19, 20
6, 10, 14, 15, 15

Explanation:

Step1: Calculate mean for each dataset

Mean formula: $\frac{\sum_{i = 1}^{n}x_{i}}{n}$

• For $11,11,13,15,20$: $\frac{11 + 11+13+15+20}{5}=\frac{70}{5} = 14$
• For $5,11,14,14,31$: $\frac{5+11+14+14+31}{5}=\frac{75}{5}=15$
• For $11,11,14,19,20$: $\frac{11 + 11+14+19+20}{5}=\frac{75}{5}=15$
• For $6,10,14,15,15$: $\frac{6+10+14+15+15}{5}=\frac{60}{5}=12$

Step2: Check median (middle - value of ordered dataset)

• For $5,11,14,14,31$: median is $14$
• For $11,11,14,19,20$: median is $14$

Step3: Check mode (most - frequent value)

• For $5,11,14,14,31$: mode is $14$
• For $11,11,14,19,20$: mode is $11$

Answer:

$11,11,14,19,20$