consider the following sample data, which represent weights of sea mussels grown on the california coast, in…

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.

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.

Answer

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