Question 19·Easy·One-Variable Data Distributions; Measures of Center and Spread
A study was conducted on the production rates for a company that produces tractor wheels. The table below shows the number of wheels made during 11 consecutive one-hour production periods.
| One-hour period | Number of wheels made |
|---|---|
| A | 24 |
| B | 24 |
| C | 21 |
| D | 21 |
| E | 21 |
| F | 19 |
| G | 24 |
| H | 24 |
| I | 19 |
| J | 22 |
| K | 23 |
What is the range of the number of wheels made for the 11 one-hour periods?
For range questions, ignore the order and frequencies and focus only on the extreme values: scan the data to find the single largest and single smallest numbers, then subtract smallest from largest. Because the SAT often uses decimal answer formats (like 5.0 instead of 5), always compare your result to the choices carefully and choose the numerically equivalent option.
Hints
Focus on definitions
Recall that the range of a data set is found by comparing the largest and smallest values. It does not use the middle or average values.
Find the extremes
From the "Number of wheels made" column, which one-hour period had the highest number of wheels? Which had the lowest?
Use subtraction
Once you know the highest and lowest numbers of wheels made, subtract the smaller number from the larger number to get the range.
Desmos Guide
Enter the data values
In Desmos, type the list of wheel counts as L = [24,24,21,21,21,19,24,24,19,22,23] and press Enter.
Compute the range with max and min
On a new line, type max(L) - min(L) and press Enter. The output number is the range of the data set; match this value to the closest option in the answer choices.
Step-by-step Explanation
Identify the largest value in the table
Look through the "Number of wheels made" column and find the greatest number.
The numbers are: 24, 24, 21, 21, 21, 19, 24, 24, 19, 22, 23.
The largest of these values is .
Identify the smallest value in the table
Now find the smallest number in that same column.
From the list 24, 24, 21, 21, 21, 19, 24, 24, 19, 22, 23, the smallest value is .
Compute the range
The range of a data set is defined as:
Substitute the values you found:
In the answer choices, this is written as , so the correct answer is 5.0.