Statistical Description of DataMTP March 22Question 2783 of 295
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Cost of sugar in a month under the heads raw Materials, labour, direct production and others were 12,20,35\displaystyle 12, 20, 35 and 23\displaystyle 23 units respectively. What is the diff. between the central angles for the largest and smallest components of the cost of sugar?

Options

A72∘\displaystyle 72^\circ
B48∘\displaystyle 48^\circ
C56∘\displaystyle 56^\circ
D92∘\displaystyle 92^\circ
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Correct Answer

✅ Option d — 92∘\displaystyle 92^\circ

All Options:

  • A72∘\displaystyle 72^\circ
  • B48∘\displaystyle 48^\circ
  • C56∘\displaystyle 56^\circ
  • D92∘\displaystyle 92^\circ

Detailed Solution & Explanation

The component costs are: - Raw Materials = 12\displaystyle 12 units - Labour = 20\displaystyle 20 units - Direct Production = 35\displaystyle 35 units - Others = 23\displaystyle 23 units Total components sum = 12+20+35+23=90\displaystyle 12 + 20 + 35 + 23 = 90 units. Since the total central angle in a pie chart is 360∘\displaystyle 360^\circ, each unit corresponds to: 360∘90=4∘\frac{360^\circ}{90} = 4^\circ The largest component is Direct Production (35\displaystyle 35 units) and the smallest component is Raw Materials (12\displaystyle 12 units). The difference in units = 35−12=23\displaystyle 35 - 12 = 23 units. The difference between their central angles is: Difference=23×4∘=92∘\text{Difference} = 23 \times 4^\circ = 92^\circ This corresponds to Option D. Hence, **Option D** is the correct answer.

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