Data Interpretation

- 1. Bar Charts
- 2. Simple Bar Chart
- 3. Composite Bar Chart
- 4. The Use of Bar Charts to Show Deviations
- 5. Representation of Percentage on a Stacked Bar Chart
- 6. Example

Bar charts are one of the easiest, graphically attractive and hence most commonly used methods of presenting all types of data. They are especially useful for representing various data series. The data series comprises the continuous variables while the values of the specific instances at which the value of the data series is measured represents the values of the discrete variables.

Presentation of data as bar charts makes the comparative study of the data very easy. A bar chart consists of a group of bars which are equidistant from each other. The values on the bar charts are read by the measurement of the length or the height of the bars. The width of the bars is largely inessential and is used only for the clarity of the presentation.

Now let's have a look onto the different kinds of bar charts and the kinds of data that can be represented on a bar-chart.

The simple bar chart is the simplest bar chart which has one continuous variable charted along with one discrete variable. Figure below shows an example of *Simple Bar Chart.*

One of the primary limitations of the simple bar chart is that it can only be used to display a single continuous variable. If two or more sets of continuous variables are to be shown on the same bar chart, we use what is called a composite bar-chart. Figure below shows an example of the *Composite Bar Chart.*

Deviation bars are useful for graphic presentation of continuous variables which can have both positive and negative values, i.e., surplus or deficit, net profit or loss, net of imports and exports. In general continuous variables which have both positive and negative values are best represented on bar charts.

A base line is created and positive values (such as profit, surplus), etc., are represented by hers above the base line while negative deviations (loss or deficit) are represented by bars below the base line as shown in the figure above.

Sometimes stacked bars can also be used to represent the break-up of some continuous variable. Figure below will make it clear.

Such a use of bar charts is quite convenient for comparing two or more sets of data.

Figure below shows the break-up of the various sources of revenues for the Government of India over a two-year period.

Answer the question based on the chart below.

In how many of the given years was the exports at least 10% more than the imports?

**(A)** 0 **(B) **1 **(C)** 2 **(D)** 3 **(E)** 4

**Solution:**

In 1994, exports $= 80 > 70\dfrac{10}{100}(70) = 77$

in 1995, exports $= 130

in i996, exports

=> We need not consider this year

In l997, exports $= 112 > 100 + \dfrac{10}{100}(100)= 110$

In 1998, exports $= 170

In 1999, exports $= 160

=> The given condition was satisfied in two years.

Choice **(C) **is the correct answer.

What was the average exports for the given period (in Ã¢â‚¬Ëœ000 crores)?

**(A)** 145 **(B)** 132 **(C)** 126 **(D) **119 **(E)** 138

Average exports:

$= \dfrac{80+130+140+112 + 170 + 160}{6} = 132$

Thus choice **(B)** is the right answer.

From 1995 to 1999, in which year was the percentage growth In exports, when compared to the previous year, the highest?

**(A)** 1995 **(B)** 1996 **(C)** 1997 **(D)** 1998 **(E) **1999

Export in a year exceeded that in the previous year in 1995, I996 and I998. Percentages by which exports in I995, I996 and 1998 exceed the exports in the previous year were:

$\left(\dfrac{50}{80}\right)100\%, \left(\dfrac{10}{130}\right)100\%$ and $\left(\dfrac{58}{112}\right)100\%$ respectively.

Only in I995 was the growth more than 60%

Thus choice **(A) **is the correct answer.

What is the simple average annual growth rate in the imports from I994 to 1999?

**(A)** 15 **(B)** 18 **(C)** 19 **(D)** 21 **(E)** 23

Imports in 1994 (in '000 crores) = 70

Imports in 1999 (in '000 crores) = 150

Percentage growth $= \left(\dfrac{150 - 70}{70}\right)100 = 115\%$

Average annual growth $= \dfrac{115}{5} = 23$

Thus choice **(E) **is the correct answer.

Among the years in which the imports as well as exports exceed those in the previous years, In how many years was the percentage increase in imports less than the percentage increase in exports?

**(A)** 0 **(B)** 1 **(C)** 2 **(D)** 3 **(E)** 4

The imports as well as exports exceeded those in the previous years in I995, I996 and 1998. In none of the years was the given condition satisfied.

Thus choice **(A) **is the correct answer.