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. 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: Calculate sum of data

The sum of the data set \(1.4 + 1.5+1.7 + 2+2.1\times4+2.2\times2+2.3\times3+2.4\times2+2.5\times2+2.7+2.9\)
\[=1.4 + 1.5+1.7+2+(2.1\times4)+(2.2\times2)+(2.3\times3)+(2.4\times2)+(2.5\times2)+2.7+2.9\]
\[=1.4 + 1.5+1.7+2 + 8.4+4.4+6.9+4.8+5+2.7+2.9\]
\[=(1.4 + 1.5+1.7+2)+(8.4+4.4+6.9+4.8+5+2.7+2.9)\]
\[=6.6+35.1=41.7\]

Step2: Calculate number of data points

There are \(n = 20\) data - points.

Step3: Calculate mean

The mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}=\frac{41.7}{20}=2.085\) (This was an incorrect input in the original problem, but correct calculation).

Step4: Find mode

The mode is the number that appears most frequently in the data - set. The number \(2.1\) appears \(4\) times, which is more frequently than any other number in the data - set.

Answer:

Mean: \(2.085\)
Median: \(2.2\)
Mode: \(2.1\)