Question 10·Easy·One-Variable Data Distributions; Measures of Center and Spread
Number of High School Students Who Completed Summer Internships
| High school | 2008 | 2009 | 2010 | 2011 | 2012 |
|---|---|---|---|---|---|
| Foothill | 87 | 80 | 75 | 76 | 70 |
| Valley | 44 | 54 | 65 | 76 | 82 |
| Total | 131 | 134 | 140 | 152 | 152 |
The table above shows the number of students from two different high schools who completed summer internships in each of five years. No student attended both schools.
Which of the following statements are true about the number of students who completed summer internships for the 5 years shown?
I. The mean number from Foothill High School is greater than the mean number from Valley High School.
II. The median number from Foothill High School is greater than the median number from Valley High School.
For questions comparing means and medians of small data sets, quickly write each school's numbers, compute the mean by summing and dividing by the count, and find the median by ordering the numbers and picking the middle value. Keep your work organized in two clear columns (one for each group), and compare the computed values directly to the statements instead of trying to guess from the table. This minimizes mistakes and lets you decide which statements are true in under a minute.
Hints
Focus on what each statement is asking
Statement I is about the mean (average) for each school over the 5 years; Statement II is about the median (middle value) for each school over the 5 years. Handle them one at a time.
Calculate the means
For each school, add its 5 yearly numbers and divide by 5. Then compare the two means to see which is larger.
Find the medians
Write each school’s 5 numbers in increasing order, then find the middle (3rd) number in each list and compare those two medians.
After computing, match to statements I and II
Decide whether each statement (about mean and median) is true based on the values you found, then pick the choice that matches which statements are true.
Desmos Guide
Enter the data as lists
Type F = [87,80,75,76,70] for Foothill and V = [44,54,65,76,82] for Valley.
Use Desmos to compute the means
On a new line, type mean(F) and mean(V). Compare the two outputs to see which mean is greater.
Use Desmos to compute the medians
On another line, type median(F) and median(V). Compare these outputs to see which median is greater, then decide which statements (I and II) are true based on those comparisons.
Step-by-step Explanation
Recall what mean and median mean
- Mean: Add all the numbers in a set and divide by how many numbers there are.
- Median: List the numbers in order and pick the middle one (for 5 numbers, it is the 3rd number in the ordered list).
Compute the mean for each school
Foothill:
Numbers:
Sum:
Mean:
Valley:
Numbers:
Sum:
Mean:
So Foothill’s mean is and Valley’s mean is .
Find the median for each school
To find the median, order each school’s numbers from least to greatest and take the middle (3rd) value.
Foothill:
Ordered data:
- The median (3rd number) is .
Valley:
Ordered data:
- The median (3rd number) is .
So Foothill’s median is and Valley’s median is .
Match your results to the statements and choose the answer
Now compare your results to the statements:
- Statement I talks about the means. Foothill’s mean is and Valley’s mean is , so Foothill’s mean is greater.
- Statement II talks about the medians. Foothill’s median is and Valley’s median is , so Foothill’s median is greater.
Both statements I and II are true, so the correct answer choice is I and II.