Question

consider the following sample data, which represent weights of sea mussels grown on the california coast, in grams: { 1.5, 1.7, 2, 2, 2.1, 2.2, 2.3, 2.3, 2.3, 2.4, 2.5, 2.5, 2.7, 2.7, 2.8, 2.8, 3, 3.1, 3.1 }. first, give the mean of the data set. next, give the median of the data set.

Explanation:

Step1: Calculate the mean

The formula for 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, $n = 20$, and $\sum_{i=1}^{20}x_i=1.5 + 1.7+2+2+2.1+2.2+2.3+2.3+2.3+2.4+2.5+2.5+2.7+2.7+2.8+2.8+3+3.1+3.1=46$. So, $\bar{x}=\frac{46}{20}=2.3$.

Step2: Calculate the median

First, arrange the data in ascending order (which it already is). Since $n = 20$ (an even - numbered data set), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered observations. $\frac{n}{2}=10$ and $\frac{n}{2}+1 = 11$. The 10th value is $2.3$ and the 11th value is $2.4$. So, the median $M=\frac{2.3 + 2.4}{2}=2.35$.

Answer:

2.35