Question

1. calculate the mean for the following set of data: {\frac{1}{4}, \frac{3}{4}, \frac{5}{4}, \frac{7}{4}, \frac{3}{4}, \frac{11}{4}} a) \frac{7}{4} b) \frac{5}{2} c) \frac{5}{4} d) \frac{1}{6}

Explanation:

Step1: Recall mean formula

The mean $\bar{x}$ of a data - set $x_1,x_2,\cdots,x_n$ is $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$. Here $n = 6$, and $x_1=\frac{1}{4},x_2=\frac{3}{4},x_3=\frac{5}{4},x_4=\frac{7}{4},x_5=\frac{3}{4},x_6=\frac{11}{4}$.

Step2: Calculate the sum of data

$\sum_{i=1}^{6}x_i=\frac{1 + 3+5 + 7+3 + 11}{4}=\frac{30}{4}$.

Step3: Calculate the mean

$\bar{x}=\frac{\frac{30}{4}}{6}=\frac{30}{4}\times\frac{1}{6}=\frac{30}{24}=\frac{5}{4}$.

Answer:

c) $\frac{5}{4}$