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Worked Examples · Example 5
Q.

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 (xx)01234
Number of days (ff)491485
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Step 1 — Build the cumulative frequency table.

xxffc.f.
044
1913
21427
3835
4540

Check: ∑f=4+9+14+8+5=40\sum f=4+9+14+8+5=40, matching the stated 40 days.

Step 2 — Locate the median. N=40N=40 is even, so the median is the average of the 20th and 21st observations. The c.f. after x=1x=1 is 13 (observations 1–13), and the c.f. after x=2x=2 is 27 (observations 14–27). Both the 20th and the 21st observation fall in this second group, so both equal 2. Median M=(2+2)/2=2M = (2+2)/2 = 2.

Step 3 — Find ∣x−M∣|x-M| and f∣x−M∣f|x-M| for each row.

| xx | ff | ∣x−2∣|x-2| | f∣x−2∣f|x-2| |

|---|---|---|---|

| 0 | 4 | 2 | 8 |

| 1 | 9 | 1 | 9 |

| 2 | 14 | 0 | 0 | …

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