Question

peter wants to estimate the mean value rolled on a fair number cube. he has generated four samples containing five rolls of the number cube as shown in the table below. which sample will result in the greatest mean?

sample data
sample 1 4 5 2 4 3
sample 2 2 2 6 5 6
sample 3 4 6 3 4 2
sample 4 5 2 4 3 6

sample 1
sample 2
sample 3
sample 4

Explanation:

Step1: Calculate mean of Sample 1

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. For Sample 1 with data $4,5,2,4,3$, $n = 5$, and $\sum_{i=1}^{5}x_{i}=4 + 5+2 + 4+3=18$. So the mean $\bar{x}_1=\frac{18}{5}=3.6$.

Step2: Calculate mean of Sample 2

For Sample 2 with data $2,2,6,5,6$, $n = 5$, and $\sum_{i = 1}^{5}x_{i}=2+2 + 6+5+6=21$. So the mean $\bar{x}_2=\frac{21}{5}=4.2$.

Step3: Calculate mean of Sample 3

For Sample 3 with data $4,6,3,4,2$, $n = 5$, and $\sum_{i=1}^{5}x_{i}=4 + 6+3+4+2=19$. So the mean $\bar{x}_3=\frac{19}{5}=3.8$.

Step4: Calculate mean of Sample 4

For Sample 4 with data $5,2,4,3,6$, $n = 5$, and $\sum_{i = 1}^{5}x_{i}=5+2 + 4+3+6=20$. So the mean $\bar{x}_4=\frac{20}{5}=4$.

Answer:

B. Sample 2