Question

consider the following sample data, which represent weights of sea mussels grown on the california coast, in grams: { 1.8, 1.8, 1.9, 2, 2.1, 2.1, 2.2, 2.2, 2.3, 2.3, 2.3, 2.3, 2.3, 2.4, 2.6, 2.8, 2.9, 3, 3 }. first, give the mean of the data set. 2.2 part 2 of 5 next, give the median of the data set.

Explanation:

Step1: Count data - points

The data - set has $n = 20$ values.

Step2: Arrange data in ascending order

The data is already in ascending order: $\{1.8, 1.8, 1.9, 2, 2.1, 2.1, 2.2, 2.2, 2.3, 2.3, 2.3, 2.3, 2.3, 2.4, 2.6, 2.8, 2.9, 3, 3\}$.

Step3: Find median position

For a data - set with $n$ values (where $n$ is even), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+ 1)$th ordered values. Here, $\frac{n}{2}=\frac{20}{2}=10$ and $\frac{n}{2}+1 = 11$.

Step4: Identify median values

The 10th value is $2.3$ and the 11th value is $2.3$.

Step5: Calculate median

Median $=\frac{2.3 + 2.3}{2}=2.3$.

Answer:

$2.3$