Question

five eretmochelys imbricata, a type of sea turtle, each have a nest. the table shows an original data set of the number of eggs that each turtle laid in its nest. nest number of eggs a 149 b 144 c 148 d 136 e 139 a sixth nest with 121 eggs is added to create a new data set. which of the following correctly compares the means of the two data sets? a the mean of the original data set is greater than the mean of the new data set.

Explanation:

Step1: Calculate original - data - set mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. For the original data - set with $n = 5$ and $x_1=149,x_2 = 144,x_3=148,x_4=136,x_5=139$.
$\sum_{i = 1}^{5}x_{i}=149 + 144+148+136+139=716$.
The mean of the original data - set $\bar{x}_1=\frac{716}{5}=143.2$.

Step2: Calculate new - data - set mean

A new data - point $x_6 = 121$ is added, so $n = 6$ and $\sum_{i = 1}^{6}x_{i}=716+121 = 837$.
The mean of the new data - set $\bar{x}_2=\frac{837}{6}=139.5$.

Step3: Compare the means

Since $143.2>139.5$, the mean of the original data set is greater than the mean of the new data set.

Answer:

A. The mean of the original data set is greater than the mean of the new data set.