Question 22·Easy·One-Variable Data Distributions; Measures of Center and Spread
Five Smallest Countries in 2016
| Country | Land area (square kilometers) |
|---|---|
| Monaco | 2.0 |
| Nauru | 21 |
| San Marino | 61 |
| Tuvalu | 26 |
| Vatican City | 0.44 |
The table above shows the land area, in square kilometers, of the five smallest countries of the world in 2016. Based on the table, what is the mean land area of the 5 smallest countries in 2016, to the nearest square kilometer?
For mean/average questions with a small table, first count how many data points there are, then add them efficiently (grouping easy pairs like or ) to reduce errors. After you get the total, divide by the count, and finally apply any rounding instructions (such as to the nearest whole number). Always double-check that you used all entries in the table and that you are not accidentally stopping at the sum instead of dividing to find the mean.
Hints
Recall the definition of mean
Mean (average) is found by adding all the data values and then dividing by how many values there are. How many countries are in the table?
Combine all the land areas
Write all 5 land areas in an addition expression, including the decimal . Add them carefully—keeping decimal points lined up can help.
Use the correct denominator
After you find the total land area, divide that total by (since there are 5 countries). This gives you the mean before rounding.
Rounding step
Once you have the mean as a decimal, think about whether its decimal part is less than or at least to decide how to round to the nearest whole number.
Desmos Guide
Compute the mean in Desmos
Type the expression (2 + 21 + 61 + 26 + 0.44) / 5 into a Desmos expression line. Look at the numerical result Desmos gives you, then round that value to the nearest whole number to match the question’s units (square kilometers).
Step-by-step Explanation
Recall what mean (average) means
The mean (average) of a set of numbers is found by adding all the numbers together and then dividing that total by how many numbers there are.
Here, there are 5 countries, so you will:
- Add their land areas.
- Divide the sum by .
Add the 5 land areas
Add the land areas (including the decimal value) from the table:
So, the total land area of the 5 countries is square kilometers.
Divide by the number of countries
Now divide the total by (because there are 5 countries) to get the mean:
So the mean land area is square kilometers before rounding.
Round to the nearest square kilometer and choose the answer
The decimal is closest to when rounding to the nearest whole number, because the decimal part is less than .
Therefore, the mean land area of the 5 smallest countries, to the nearest square kilometer, is 22, which corresponds to choice B.