Question 511·Easy·Math

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Five Eretmochelys imbricata, a type of sea turtle, each have a nest. The table shows 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?

An extra value added to a data set can change its mean, the total divided by the number of values. Enter the original egg counts as a Desmos list and find their mean, then add the sixth count and check the new mean. Don't treat adding a nest as replacing one: the new set has one more value.

Hints

Hint 1
Each row of the table gives one nest's egg count. Put all five counts in a Desmos list, then use the mean function to find the original average.
Hint 2
The sixth nest is added, so the new list must have six counts. Is its egg count above or below the original mean? A value below the old mean pulls the new mean down.

Step-by-step

Compare the means with Desmos lists
Step 1
Find the original mean
The mean is the total number of eggs divided by the number of nests. The table gives one count per nest, so type $a=[149,144,148,136,139]$ , then $\operatorname{mean}(a)$ . Desmos shows $143.2$ eggs per nest for the original five nests.
Step 2
Find the mean with the sixth nest
The nest with $121$ eggs is added, not substituted for another nest. Type $b=[149,144,148,136,139,121]$ , then $\operatorname{mean}(b)$ . Desmos shows $139.5$ eggs per nest across all six nests.
Step 3
Compare the two means
The new $121$ -egg nest has fewer eggs than the original mean of $143.2$ . Adding a value below the old mean pulls the mean down. The original mean, $143.2$ eggs per nest, is greater than the new mean, $139.5$ eggs per nest. Choice D.

Question 511·Easy·Math

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