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. 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. b) the mean of the original data set is less than the mean of the new data set. c) the means of both data sets are equal. d) there is not enough information to compare the means.

Explanation:

Step1: Calculate original mean

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

Step2: Calculate new mean

A new value $x_6 = 121$ is added, so $n = 6$. The new sum is $\sum_{i = 1}^{6}x_{i}=716+121 = 837$. The new mean $\bar{x}_2=\frac{837}{6}=139.5$.

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.