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Zorluk: Çok zorStatistical Maps and Graphical Representation

A statistical table shows the annual agricultural crop production for a region in Nigeria as follows:

CropProduction (metric tonnes)
Cocoa540540
Oil Palm360360
Rubber180180
Groundnut120120

If this data is to be represented using a pie chart, what is the exact difference between the central angle allocated to Cocoa and the combined central angle allocated to Rubber and Groundnut?

  1. 72∘72^\circCevap
  2. B
    90∘90^\circ
  3. C
    144∘144^\circ
  4. D
    162∘162^\circ

Cevap

The difference between the central angle allocated to Cocoa and the combined central angle allocated to Rubber and Groundnut is 72∘72^\circ.
The total commodity output equals 12001200 tonnes. The sector angle for Cocoa is calculated as 5401200×360∘=162∘\frac{540}{1200} \times 360^\circ = 162^\circ. The combined tonnage for Rubber and Groundnut is 180+120=300180 + 120 = 300 tonnes, giving a combined angle of 3001200×360∘=90∘\frac{300}{1200} \times 360^\circ = 90^\circ. The difference between these two values is 162∘−90∘=72∘162^\circ - 90^\circ = 72^\circ.

Adım Adım Çözüm

1
Calculate the total crop production
Total=540+360+180+120=1200 metric tonnes\text{Total} = 540 + 360 + 180 + 120 = 1200\text{ metric tonnes}
The total dataset value is required to determine the proportional weight of each commodity.
2
Calculate the central sector angle for Cocoa
AngleCocoa=(5401200)×360∘=0.45×360∘=162∘\text{Angle}_{\text{Cocoa}} = \left(\frac{540}{1200}\right) \times 360^\circ = 0.45 \times 360^\circ = 162^\circ
A pie chart represents total data as a 360∘360^\circ circle.
3
Calculate the combined central sector angle for Rubber and Groundnut
Combined Production=180+120=300 metric tonnes\text{Combined Production} = 180 + 120 = 300\text{ metric tonnes}; AngleCombined=(3001200)×360∘=0.25×360∘=90∘\text{Angle}_{\text{Combined}} = \left(\frac{300}{1200}\right) \times 360^\circ = 0.25 \times 360^\circ = 90^\circ
Summing the metric tonnage of the two minor crops allows direct conversion to their aggregated sector angle.
4
Determine the difference between the angles
162∘−90∘=72∘162^\circ - 90^\circ = 72^\circ
Subtracting the combined angle from the primary crop angle yields the required angular difference.

Anahtar Kavram

Calculation of Sector Angles for Pie Charts
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Konular

Statistical Maps and Graphical Representation

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