Question 4·Easy·One-Variable Data Distributions; Measures of Center and Spread
The high temperature, in degrees Fahrenheit (°F), in a certain city was recorded for each of 5 days. The data are shown below.
| Day | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| High temperature (°F) | 81 | 80 | 81 | 81 | 82 |
Over this 5-day period, which of the following is NOT equal to 81 °F?
For questions about measures of center and spread, first rewrite the data in order. Quickly recall definitions: mean is the average, median is the ordered middle value, mode is the most frequent value, and range is highest minus lowest. Compute each measure efficiently—often you can do small sums and differences mentally—and then compare them to what the question asks for (here, which one is not equal to a given number). Staying organized and doing quick checks (like verifying your total before dividing for the mean) helps avoid careless mistakes.
Hints
Put the data in order
Try rewriting the temperatures from least to greatest. This will make several of the statistics easier to find.
Recall what each term means
Mean is the average, median is the middle value in the ordered list, mode is the most frequent value, and range involves the highest and lowest values.
Compute each statistic numerically
Actually calculate the mean, median, mode, and the difference between the largest and smallest values. Then compare each result to 81°F.
Match your results to the choices
Once you have four numbers, see which choice names the measure whose value is different from 81°F.
Desmos Guide
Enter the temperature data as a list
Type L1 = [81, 80, 81, 81, 82] into Desmos. This stores all five temperatures in a list named .
Use Desmos to verify mean and median
On new lines, type mean(L1) and median(L1). Desmos will display the numerical values of the mean and median; compare these to 81°F.
Check the smallest and largest values
Type min(L1) and max(L1) to see the lowest and highest temperatures. Subtract the two values (either in your head or by entering max(L1) - min(L1)) to find the range, and see whether this result matches 81°F.
Determine the mode visually
Look at the list and count how many times each temperature appears. Identify which value occurs most often and compare that value to 81°F. Then decide which of the four measures is the one that does not match 81°F.
Step-by-step Explanation
Organize the temperature data
Write the temperatures in order from least to greatest: 80, 81, 81, 81, 82.
This makes it easier to find the median, mode, and range.
Find the median, mode, and mean
Median: For 5 numbers in order, the median is the 3rd number. The 3rd number in is 81, so the median is 81°F.
Mode: The mode is the value that appears most often. 81 appears 3 times, more than any other number, so the mode is 81°F.
Mean: Add the temperatures and divide by 5.
So the mean is 81°F.
Find the range
The range is the difference between the highest and lowest values.
- Lowest temperature: 80°F
- Highest temperature: 82°F
So the range is
The range is 2°F.
Answer the question
The question asks which measure is not equal to 81°F.
- Median: 81°F
- Mean: 81°F
- Mode: 81°F
- Range: 2°F
The only measure that is not 81°F is the range of the high temperatures, which corresponds to choice D.