Question

consider the following sample data, which represent weights of sea mussels grown on the california coast, in grams: { 1.4, 1.5, 1.7, 2, 2.1, 2.1, 2.1, 2.1, 2.2, 2.2, 2.3, 2.3, 2.3, 2.4, 2.4, 2.5, 2.5, 2.7, 2.9 }. first, give the mean of the data set.

Explanation:

Step1: Count data points

There are 20 data - points in the set.

Step2: Sum of data points

$1.4 + 1.5+1.7 + 2+2.1\times4+2.2\times2+2.3\times3+2.4\times2+2.5\times2+2.7+2.9$
$=1.4 + 1.5+1.7 + 2+(2.1\times4)+(2.2\times2)+(2.3\times3)+(2.4\times2)+(2.5\times2)+2.7+2.9$
$=1.4 + 1.5+1.7 + 2 + 8.4+4.4+6.9+4.8+5+2.7+2.9$
$=(1.4 + 1.5+1.7 + 2)+8.4+4.4+6.9+4.8+5+2.7+2.9$
$=6.6+8.4+4.4+6.9+4.8+5+2.7+2.9$
$=(6.6 + 8.4)+4.4+6.9+4.8+5+2.7+2.9$
$=15+4.4+6.9+4.8+5+2.7+2.9$
$=(15 + 4.4)+6.9+4.8+5+2.7+2.9$
$=19.4+6.9+4.8+5+2.7+2.9$
$=(19.4 + 6.9)+4.8+5+2.7+2.9$
$=26.3+4.8+5+2.7+2.9$
$=(26.3 + 4.8)+5+2.7+2.9$
$=31.1+5+2.7+2.9$
$=(31.1 + 5)+2.7+2.9$
$=36.1+2.7+2.9$
$=(36.1 + 2.7)+2.9$
$=38.8+2.9$
$=41.7$

Step3: Calculate the mean

The mean $\bar{x}=\frac{\text{Sum of data points}}{\text{Number of data points}}=\frac{41.7}{20}=2.085$

Answer:

$2.085$