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The distribution of Junior workers is as follow: Clerks - 78, Drivers - 36, Typists - 44, Messengers - 52, other - 30. Represent the above information by a pie chart. b. The table below show the frequency distribution of marks scored by 30 Candidates in a operate test.

Mathematics

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Step-by-step solution

3 steps
  1. Calculate the total number of junior workers.

    Total workers=78(Clerks)+36(Drivers)+44(Typists)+52(Messengers)+30(Other)\text{Total workers} = 78 (\text{Clerks}) + 36 (\text{Drivers}) + 44 (\text{Typists}) + 52 (\text{Messengers}) + 30 (\text{Other}) Total workers=240\text{Total workers} = 240
  2. Calculate the angle for each category in the pie chart.

    The total angle in a circle is 360∘360^\circ.
    The formula for the angle of a sector is:

    Angle=(Number in categoryTotal workers)×360∘\text{Angle} = \left( \frac{\text{Number in category}}{\text{Total workers}} \right) \times 360^\circ
    • Clerks:
    Angle for Clerks=(78240)×360∘=0.325×360∘=117∘\text{Angle for Clerks} = \left( \frac{78}{240} \right) \times 360^\circ = 0.325 \times 360^\circ = 117^\circ
    • Drivers:
    Angle for Drivers=(36240)×360∘=0.15×360∘=54∘\text{Angle for Drivers} = \left( \frac{36}{240} \right) \times 360^\circ = 0.15 \times 360^\circ = 54^\circ
    • Typists:
    Angle for Typists=(44240)×360∘=0.1833...×360∘=66∘\text{Angle for Typists} = \left( \frac{44}{240} \right) \times 360^\circ = 0.1833... \times 360^\circ = 66^\circ
    • Messengers:
    Angle for Messengers=(52240)×360∘=0.2166...×360∘=78∘\text{Angle for Messengers} = \left( \frac{52}{240} \right) \times 360^\circ = 0.2166... \times 360^\circ = 78^\circ
    • Other:
    Angle for Other=(30240)×360∘=0.125×360∘=45∘\text{Angle for Other} = \left( \frac{30}{240} \right) \times 360^\circ = 0.125 \times 360^\circ = 45^\circ
  3. Summarize the angles for the pie chart.

    • Clerks: 117∘\mathbf{117^\circ}
    • Drivers: 54∘\mathbf{54^\circ}
    • Typists: 66∘\mathbf{66^\circ}
    • Messengers: 78∘\mathbf{78^\circ}
    • Other: 45∘\mathbf{45^\circ}

    These angles sum to 117∘+54∘+66∘+78∘+45∘=360∘117^\circ + 54^\circ + 66^\circ + 78^\circ + 45^\circ = 360^\circ.

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