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. part 2 of 5 next, give the median of the data set. part 3 of 5 now give the mode of the data set. if there is more than one, write them in order, separated by commas. part 4 of 5 give the midrange of the data set. part 5 of 5 given the relationship between the mean and median above, what shape is the distribution likely to be? the distribution will probably be skewed to the left. the distribution will probably be skewed to the right. the distribution will be roughly symmetric.

Explanation:

Step1: Calculate the 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, $n = 20$, and $\sum_{i=1}^{20}x_{i}=1.4 + 1.7\times2+1.8\times3 + 1.9+2+2.1+2.2\times6+2.3+2.4+2.6+2.9+3=40.8$. So, $\bar{x}=\frac{40.8}{20}=2.04$.

Step2: Find the median

The data is already in ascending order. Since $n = 20$ (an even number), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data - points. $\frac{n}{2}=10$ and $\frac{n}{2}+1 = 11$. The 10th and 11th values are both $2.2$, so the median $M = 2.2$.

Step3: Determine the mode

The mode is the most frequently occurring value. The value $2.2$ appears 6 times, more frequently than any other value, so the mode is $2.2$.

Step4: Calculate the mid - range

The mid - range is given by $\frac{\text{Min}+\text{Max}}{2}$. The minimum value $\text{Min}=1.4$ and the maximum value $\text{Max}=3$. So, the mid - range $=\frac{1.4 + 3}{2}=2.2$.

Step5: Analyze the distribution shape

Since the mean ($2.04$) is less than the median ($2.2$), the distribution will probably be skewed to the left.

Answer:

Part 1: $2.04$
Part 2: $2.2$
Part 3: $2.2$
Part 4: $2.2$
Part 5: The distribution will probably be skewed to the left.