Pie Chart

Definition: This is a circle which is divided into sectors, whose angles are used to represent data. The size of the angle of each sector gives the frequency. A pie chart is useful in comparing the size of each part in relation to the whole.

Hint:

(i) Always give your pie chart a title

(ii) You need to use your protractor to draw the angles accurately. Check the sum of the angles = 360^o.

(iii) Label each sector clearly, but it is not compulsory to write the angles on the graph.

Example 1

The pie chart below shows the weekly sales of a motor dealer in Lagos in 1999.

(a) What fraction of the cars were Toyota?

(b)What percentage of the cars were Datsun?

(c) If the dealer sold 16 Peugeot, how many BMW did he sell in a week?

Solution:

(a) Let 360^o ≡1

Toyota has angle = 120^o

i.e. 120^o ≡ x

Therefore, the fractional part of Toyota = \( \frac{120}{360} \scriptsize \; \times \; 1 = \frac{12}{36}= \frac{1}{3} \)

(b) Datsun has 90^o angle 

Let 360^o ≡ 100%

i.e. 90^o ≡ x%

∴    x% = \( \frac{90}{360} \scriptsize \; \times \; 100 \)

x% = \( \frac{1}{4} \scriptsize \; \times \; 100 = 25% \)

(c) The sectorial angle of Peugeot = 360 – (120 + 90 + 70)

     = 360^o  – 280^o

      = 80^o

i.e. 80^o ≡ 16 Peugeot Cars

also   70^o ≡x BMW Cars

∴      x number of BMW = 16 × \( \frac{70}{80}\)

= 2 ×7

= 14 BMW Cars.

Example 2

The pie chart below shows the number of passengers flying from London to Lagos on one morning. On that morning 1441 passengers flew this route altogether.

(a)How many passengers flew:

(i) Nigerian Airways?

(ii) British Airways?

(b) If the plane used by British Airways contains 380 seats, what percentage of the seats was not occupied? (Answer to 1d.p).

Solution:

(a) (i) Senatorial angle for Nigerian Airways = 360 – (75 + 52 + 80 + 90)

= 360 – 297

= 63^o

360^o = ≡1440 passengers

63^o = ≡x passengers

Therefore, x passengers = \( \scriptsize 1440 \; \times \; \frac{63}{360} \scriptsize = 36 \; \times \; 7 \)

= 252 passengers

i.e. 252 passengers flew Nigerian Airways.

(ii) 90^o of British Airways ≡y passengers

360^o ≡ 1440 passengers

Therefore, y passengers = \( \frac{90}{360} \; \times \; \frac{1400}{1} \scriptsize = 360 \; passengers\)

i.e. 360 passengers flew British Airways.

(b) Number of empty seats = 380 – 360 = 20 seats

Percentage (%) of  empty seats = \( \frac{20}{380} \; \times \; \frac{100}{1} \)

= \( \frac{1}{19} \scriptsize \; \times \; 100 \)

         = 5.2631578  ≈ 5.3%

Example 3

The table below shows the percentage allocation of periods on a school time table.

SUBJECTS	% ALLOCATION OF PERIOD
Mathematics	30%
Physics	18%
English	25%
Chemistry	12%
Biology	5%
Others	10%

1. Represent this information on a Pie Chart.
2. Find the number periods allotted for Chemistry if the total period is 60 periods (give your answer to the nearest whole number). (WAEC)

Solution:

SUBJECTS	PERCENTAGE (%)	ANGLE
Mathematics	30	\( \frac{30}{100} \; \times \; \frac{360}{1} \scriptsize = 108° \)
Physics	18	\( \frac{18}{100} \; \times \; \frac{360}{1} \scriptsize = 64.8° \)
English	25	\( \frac{25}{100} \; \times \; \frac{360}{1} \scriptsize = 90° \)
Chemistry	12	\( \frac{12}{100} \; \times \; \frac{360}{1} \scriptsize = 43.2° \)
Biology	5	\( \frac{5}{100} \; \times \; \frac{360}{1} \scriptsize = 18° \)
Others	10	\( \frac{10}{100} \; \times \; \frac{360}{1} \scriptsize = 36° \)
Total	100	360o

(c) Total Periods = 60

Chemistry = 12% of 60 periods

= \( \frac{12}{100} \; \times \; \frac{60}{1} = \frac{6 \times 6}{5} \)

= \( \frac{36}{5} \)

= 7.2

= 7 Periods (Nearest whole number).