- 2068 Jestha (old course) · 5 marks
Statistics of 25 days of orders
Short answer
Mean = 3 orders/day, median = 3, range = 6, sample SD ≈ 1.71 orders/day (n=25, Σx=75, Σx²=295).
The number of new orders received by a company over the first 25 working days were recorded as follows: 3, 0, 1, 4, 4, 4, 2, 5, 3, 6, 4, 5, 1, 4, 2, 3, 0, 2, 0, 5, 4, 2, 3, 3, 5. Determine arithmetic mean, median, range and standard deviation.
n = 25 values. Ordered data:
0 0 0 1 1 2 2 2 2 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 6
Frequency table
| x | f | fx | fx² |
|---|---|---|---|
| 0 | 3 | 0 | 0 |
| 1 | 2 | 2 | 2 |
| 2 | 4 | 8 | 16 |
| 3 | 5 | 15 | 45 |
| 4 | 6 | 24 | 96 |
| 5 | 4 | 20 | 100 |
| 6 | 1 | 6 | 36 |
| Total | 25 | 75 | 295 |
Arithmetic mean
x̄ = Σfx / n = 75 / 25 = 3 orders per day
Median
The median is the (n + 1)/2 = 13th value of the ordered data. Counting cumulative frequencies (3, 5, 9, 14, ...), the 13th value is 3.
Median = 3
Range
Range = largest − smallest = 6 − 0 = 6
Standard deviation
Sxx = Σx² − (Σx)²/n = 295 − 75²/25 = 295 − 225 = 70
s² = 70 / 24 = 2.917
s = √2.917 = 1.708
(With divisor n: σ² = 70/25 = 2.8, σ = 1.673.)
Answer: mean = 3, median = 3, range = 6, standard deviation ≈ 1.71 orders per day.
✓ Answer checked by Claude Sonnet 5.5
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