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Worked Examples · Example 2
Q.

In a survey of 50 employees, the number of days absent in a quarter is distributed as follows. Find the mean deviation about the mean.

Days absent (xx)01234
Number of employees (ff)51020105
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✓ Free question

Step 1 — Find the mean.

xxfffxfx
050
11010
22040
31030
4520
Total50100

xˉ=100/50=2\bar{x} = 100/50 = 2.

Step 2 — Find ∣x−xˉ∣|x-\bar{x}| and f∣x−xˉ∣f|x-\bar{x}| for each row.

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

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

| 0 | 5 | 2 | 10 |

| 1 | 10 | 1 | 10 |

| 2 | 20 | 0 | 0 |

| 3 | 10 | 1 | 10 |

| 4 | 5 | 2 | 10 |

| Total | 50 | | 40 |

Step 3 — Divide.

MD(xˉ)=∑f∣x−xˉ∣N=4050=0.8\text{MD}(\bar{x}) = \dfrac{\sum f|x-\bar{x}|}{N} = \dfrac{40}{50} = 0.8

Independent check. Re-adding the f∣x−2∣f|x-2| column in a different grouping, (10+10)+(0+10)+10=20+10+10=40(10+10)+(0+10)+10 = 20+10+10=40 — confirms the total.

✓Final answer

MD(xˉ)=40/50=0.8\text{MD}(\bar{x}) = 40/50 = 0.8 days

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