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Exercises · Q11
Q.

The number of vehicles sold per day by a car dealership over 25 days is distributed as follows. Find the mean deviation about the mean.

Vehicles sold (xx)01234
Number of days (ff)37942
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✓ Free question

Step 1 — Find the mean.

xxfffxfx
030
177
2918
3412
428
Total2545

xˉ=45/25=1.8\bar{x} = 45/25 = 1.8.

Step 2 — Find ∣x−1.8∣|x-1.8| and f∣x−1.8∣f|x-1.8|.

| xx | ff | ∣x−1.8∣|x-1.8| | f∣x−1.8∣f|x-1.8| |

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

| 0 | 3 | 1.8 | 5.4 |

| 1 | 7 | 0.8 | 5.6 |

| 2 | 9 | 0.2 | 1.8 |

| 3 | 4 | 1.2 | 4.8 |

| 4 | 2 | 2.2 | 4.4 |

| Total | 25 | | 22 |

Step 3 — Divide.

MD(xˉ)=2225=0.88\text{MD}(\bar{x}) = \dfrac{22}{25} = 0.88

Independent check. Re-adding in a different pairing, (5.4+4.4)+(5.6+4.8)+1.8=9.8+10.4+1.8=22(5.4+4.4)+(5.6+4.8)+1.8 = 9.8+10.4+1.8=22 — confirms the total.

✓Final answer

MD(xˉ)=22/25=0.88\text{MD}(\bar{x}) = 22/25 = 0.88 vehicles per day

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