Question

consider the following sample data, which represent weights of sea mussels grown on the california coast, in grams: { 1.4, 1.7, 1.7, 1.8, 1.8, 1.8, 1.9, 2, 2.1, 2.2, 2.2, 2.2, 2.2, 2.2, 2.3, 2.4, 2.6, 2.9, 3 }. first, give the mean of the data set. next, give the median of the data set. now give the mode of the data set. if there is more than one, write them in order, separated by commas.

Explanation:

Step1: Recall the formula for mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are the data - points and $n$ is the number of data - points. Here, $n = 20$.
$\sum_{i=1}^{20}x_{i}=1.4 + 1.7\times2+1.8\times3 + 1.9+2+2.1+2.2\times6+2.3+2.4+2.6+2.9+3$
$=1.4 + 3.4+5.4+1.9+2+2.1+13.2+2.3+2.4+2.6+2.9+3$
$=(1.4 + 3.4)+5.4+(1.9 + 2)+2.1+13.2+(2.3 + 2.4)+2.6+2.9+3$
$=4.8+5.4 + 3.9+2.1+13.2+4.7+2.6+2.9+3$
$=(4.8+5.4)+(3.9 + 2.1)+13.2+4.7+2.6+2.9+3$
$=10.2+6+13.2+4.7+2.6+2.9+3$
$=(10.2+6)+13.2+4.7+2.6+2.9+3$
$=16.2+13.2+4.7+2.6+2.9+3$
$=(16.2+13.2)+4.7+2.6+2.9+3$
$=29.4+4.7+2.6+2.9+3$
$=(29.4+4.7)+2.6+2.9+3$
$=34.1+2.6+2.9+3$
$=(34.1+2.6)+2.9+3$
$=36.7+2.9+3$
$=(36.7+2.9)+3$
$=39.6+3=42.6$.
$\bar{x}=\frac{42.6}{20}=2.13$.

Step2: Recall the formula for mode

The mode is the data - value that appears most frequently in a data set. In the given data set, the number $2.2$ appears 6 times, which is more frequently than any other number.

Answer:

Mean: $2.13$
Mode: $2.2$