Answer-first summary for fast verification
Answer: 2,650
To find the 25% quantile (first quartile), we need to follow these steps: 1. **Sort the data in ascending order**: - 2,600 (Week 5) - 2,700 (Week 3) - 2,800 (Week 2) - 3,800 (Week 1) - 4,300 (Week 6) - 9,900 (Week 4) 2. **Calculate the position**: - Position = α × n = 0.25 × 6 = 1.5 - Where α = 0.25 (25% quantile) and n = 6 (number of observations) 3. **Find the quantile value**: - Since 1.5 is not an integer, we take the average of the values at positions 1 and 2 - Position 1: 2,600 - Position 2: 2,700 - Average = (2,600 + 2,700) ÷ 2 = 2,650 Therefore, the 25% quantile of the profits is $2,650. **Key Points**: - The 25% quantile (Q1) represents the value below which 25% of the data falls - When the calculated position is not an integer, we interpolate between the two nearest data points - This method provides a more accurate estimate than simply taking the value at the nearest position
Author: Nikitesh Somanthe
Ultimate access to all questions.
The following data represents a sample of daily profit of a sales company for six weeks in a particular year.
| Week | Amount of the Profit($) |
|---|---|
| 1 | 3,800 |
| 2 | 2,800 |
| 3 | 2,700 |
| 4 | 9,900 |
| 5 | 2,600 |
| 6 | 4,300 |
What is the 25% quantile of the profits?
A
2750
B
2,700
C
2,650
D
2,600
No comments yet.