The number of customer complaints received per day by a company, recorded over 40 days, is given below. Find the mean deviation about the median.
| Complaints () | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Number of days () | 4 | 9 | 14 | 8 | 5 |
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Start your 14-day free trial to unlock the full solution →Step 1 — Build the cumulative frequency table.
| c.f. | ||
|---|---|---|
| 0 | 4 | 4 |
| 1 | 9 | 13 |
| 2 | 14 | 27 |
| 3 | 8 | 35 |
| 4 | 5 | 40 |
Check: , matching the stated 40 days.
Step 2 — Locate the median. is even, so the median is the average of the 20th and 21st observations. The c.f. after is 13 (observations 1–13), and the c.f. after is 27 (observations 14–27). Both the 20th and the 21st observation fall in this second group, so both equal 2. Median .
Step 3 — Find and for each row.
| | | | |
|---|---|---|---|
| 0 | 4 | 2 | 8 |
| 1 | 9 | 1 | 9 |
| 2 | 14 | 0 | 0 | …
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