Question

1-92. calculate the mean of each data set below. can you find any shortcuts that allow you to find the mean without having to do much calculation? a. 6, 10, 6, 10 b. 11, 12, 12, 13, 12 c. 0, 5, 4, 8, 0, 7

Explanation:

Step1: Recall mean formula

The mean of a data - set $x_1,x_2,\cdots,x_n$ is $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$.

Step2: Analyze data - set a

In data - set a: $6,10,6,10$. The sum of the numbers is $(6 + 10)+(6 + 10)=32$, and there are $n = 4$ numbers. So the mean is $\frac{32}{4}=8$.

Step3: Analyze data - set b

In data - set b: $11,12,12,13,12$. We can think of it as $11+(12\times3)+13$. $11 + 13=24$ and $12\times3 = 36$. The sum is $24 + 36=60$, and $n = 5$. So the mean is $\frac{60}{5}=12$.

Step4: Analyze data - set c

In data - set c: $0,5,4,8,0,7$. The sum is $0+5 + 4+8+0+7=24$, and $n = 6$. So the mean is $\frac{24}{6}=4$.

Answer:

a. Mean is 8
b. Mean is 12
c. Mean is 4