A high school science club organized a daily recycling drive over a 10-day period. The frequency table below summarizes the number of aluminum cans collected per day:
| Cans Collected Per Day | Number of Days |
|---|---|
| 10 | 2 |
| 20 | 3 |
| 30 | 3 |
| 40 | 1 |
| 50 | 1 |
What is the positive difference between the mean number of cans collected per day and the median number of cans collected per day?
- A0
- 1Answer
- C4
- D5
- E6
Answer
The positive difference between the mean and median is 1.
To find the mean, calculate the weighted sum of the products of each daily quantity and its frequency: (10 × 2 + 20 × 3 + 30 × 3 + 40 × 1 + 50 × 1) = 260. Dividing 260 by the total 10 days gives a mean of 26. To find the median, list the 10 data points in order: 10, 10, 20, 20, 20, 30, 30, 30, 40, 50. The middle two numbers are the 5th and 6th terms (20 and 30), so the median is (20 + 30) / 2 = 25. Subtracting 25 from 26 yields a positive difference of 1.
Step-by-Step Solution
Key Concept
Weighted Mean and Median from Frequency Tables
Estimated Time:1m 15s