Question 13·Easy·One-Variable Data Distributions; Measures of Center and Spread
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?
For questions comparing means when a new data point is added, either compute both means directly or reason about the effect of the new value. First, find the original mean by summing the data and dividing by the number of values. Then include the new value, update the sum and the count, and compute the new mean. If you want to save time, note that adding a value below the original mean will always lower the mean and adding a value above the original mean will always raise it, allowing you to compare without full calculation.
Hints
Recall what "mean" means
Think about how to calculate the mean (average) of a set of numbers. What two things do you need to know about the data set?
Work with the original 5 nests first
Add the egg counts for nests A through E, then divide by the number of nests (5). That gives you the mean of the original data set.
Now include the sixth nest
Add the 121 eggs from the sixth nest to your previous total and divide by 6. Now you have the mean of the new data set. Compare this value to the original mean.
Compare, don’t guess
Look at the two mean values you calculated. Decide whether the first is greater than, less than, or equal to the second, and match that relationship to one of the answer choices.
Desmos Guide
Calculate the original mean in Desmos
In Desmos, type:
(149 + 144 + 148 + 136 + 139) / 5
and note the numerical result. This is the mean of the original 5 nests.
Calculate the new mean in Desmos
Next, type:
(149 + 144 + 148 + 136 + 139 + 121) / 6
and note this numerical result. This is the mean of the new data set including the sixth nest.
Compare the two Desmos outputs
Compare the two numbers you see. Decide whether the first mean is greater than, less than, or equal to the second mean, and then choose the answer choice that describes that relationship.
Step-by-step Explanation
Understand what is being compared
We have two data sets:
- Original data set: 5 nests (A–E) with egg counts 149, 144, 148, 136, and 139.
- New data set: all 5 original nests plus a sixth nest with 121 eggs.
We need to compare the means (averages) of these two data sets. Remember, the mean of a data set is
Find the mean of the original data set
Add the egg counts from nests A–E:
.
There are 5 nests in the original data set, so the original mean is
So the mean number of eggs in the original 5 nests is .
Find the mean of the new data set with the sixth nest
Now include the sixth nest, which has 121 eggs.
-
Add this to the previous total:
.
-
There are now 6 nests total, so the new mean is
So the mean number of eggs in the new data set (with 6 nests) is .
Compare the two means and choose the correct statement
We found:
- Original mean (5 nests):
- New mean (6 nests):
Since , the mean of the original data set is greater than the mean of the new data set.
This matches answer choice D) The mean of the original data set is greater than the mean of the new data set.