Quant (Concept): PIE CHART

Quant (Concept): PIE CHART - (Angles, Values, Times)

How to handle Pie Chart

A PIE CHART is a type of graph in which a circle is divided into sectors, in which each sector represents a proportion of the whole. A pie chart looks like – you’ve guessed it right –a pie! It is a circle with various-sized ‘slices’ cut out from the center to the edge. The size of the slices shows the relative size of the categories. Pie charts use percentage or angles to show the relative sizes of various categories. In simpler words, the bigger the slice of the pie, the higher is the proportion out of the total that it represents.

Handling Angles, Percentages and Numbers

You probably won’t be surprised to find that you can solve problems related to pie charts using the properties of a circle and basic concepts of percentages. A whole circle contains 360 degrees. In a pie chart, those 360 degrees corresponds to the total of the values represented in the chart. On the other hand, the distribution might be in terms of percentages, which sums up to 100%.

Now to work with a pie chart, you may need to figure out one of the following three things:

• The size of the angle in a slice.
• The value of a slice.
• The total sum of the values in all the slices.

Important points:

• Total angle at the center of a pie chart = 360^o
• To convert k% into angle = (k/100) × 360
• To convert m^o into percentage = (m/360) ×100

ILLUSTRATION:

DIRECTIONS: The circular graph given below shows the spending by a family on various items during the year 1998. Study the graph and answer the questions that follow.

(Percent of money spent by a family during 1998)

Example 1:

If the total amount spent during the year 1998 was Rs. 46000, how much was the amount spent on food?

Solution:

Food comprises of 23% of the total spending, therefore, amount spent on food = 46000 × 23/100 = Rs 10580.

Example 2:

If the total amount spent during the year 1998 was Rs. 46000, how much was the amount spent on clothing and housing together?

Solution:

Amount spent on clothing and housing are 10% and 15%, respectively.

Therefore, total amount spent is, 46000 × 10/100 + 46000 × 15/100 = (4600 + 6900) = 11500

Note: Instead of finding the two values individually, you can sum up the percentages spent on clothing and housing i.e. (10 + 15) i.e. 25 %.

Now, the total amount spent on clothing and housing together is 46000 × 25/100 = 11500

Example 3:

What was the ratio of the total amount of money spent on housing to that spent on education?

Solution:

In this question too, there is no need to find out the amounts spent on housing or education. Instead you can get the answer by comparing the percentages i.e. 15 : 12 ⇒ 5 : 4.

Example 4:

As per the chart, the maximum amount was spent on which item, if the total expenditure was given to be Rs. 48256? 

Solution:

Irrespective of the total expenditure, the item on which maximum amount was spent will be the item on which maximum percentage of total was spent, i.e. food (23% spent).

Example 5:

The amount spent on Housing is how many times of the amount spend on transport, if the total expenditure happens to be Rs. 83000?

Solution:

You can avoid doing long calculations in this question as well. In terms of percentage, housing and transport are 15% and 5% respectively. Hence the expenditure on housing will be 15/5 = 3 times of the percentage on transport.

Learning:

How to solve simple pie-chart questions with minimum calculations.