SSC CHSL Topic Wise Study Material – Quantitative Aptitude – Bar-Diagram
Bar chart or graph is one of the oldest and most commonly used graph for presenting data. It is a chart with rectangular bars (equidistant from each other) with lengths proportional to the values they represent. The width of the bars is shown merely for attention.
In this method of data representation, the data is plotted on the x and y axis as bars.
One of the axis (normally the x-axis) of the bar diagram represents a discrete variable while the other axis represents the scale for one or more continuous variable. Each bar diagram has title indicating the subject matter represented in the diagram.
Types of Graph/Chart
1. Simple Bar Diagram A simple bar diagram relates to only one variable.
2. Sub-divided Bar Diagram A sub-divided bar diagram is used to represent various parts of total magnitude of a given variable.
3. Multiple Bar Diagram In this type, two or more bars are constructed adjoining each bar either to represent either , different components of a total or to show multiple variables.
Directions (Examples 1 -5) Study the graph and answer the questions given below. ssc (10+2)2011
1. What is the difference in profit between 1983 and 1984 (in lakh of Rs)?
(a) No profit
2. The number of years in which the income is more than the average income of the given years is
3. The ratio of the average income of all the years to the average profit is
(a) 24 :13
(b) 48 :17
(c) 12 : 7
(d) 6 : 5
4.Percentage increase in profit in 1986 over 1982 is
5. The total income exceeds the total expenditure over the years 1982 to 1986 by
(a) Rs 85 lakh
(b) Rs 105 lakh
(c) Rs 115 lakh
(d) Rs 120 lakh
Illustration for Bar Diagram
The diagram above shows the survey of 6 yr for the sales of mobile phones.
Here, x-axis shows the years which were considered for survey and y-axis shows the quantity of sales.
To understand histogram, we need to know the word frequency.
Frequency It is the number of occurrences of a repeating event per unit.
Histogram It is a representation of tabulated frequencies. This representation is done with the help of adjacent rectangles erected over discrete intervals.
Different Components of Histogram
Height of the Rectangular Bars It shows frequency density of the interval, i.e., the frequency divided by the
width of the interval.
Area Covered by the Bars This area shows the frequency of the observations in the interval.
Total Area of Histogram This area is equal to the number of data.
Directions (Examples 6-8) In the given histogram, there is survey for the different; family of different income group of a village. Study the graph carefully and answer the questions given below. ssc (1o+2) 2010
6. How many families were surveyed?
7. What is the total number of family whose daily income is Rs 800 or more?
8. What is the percentage of families whose daily income is less than Rs 500?
* If any bar has frequency zero, then no bar will be formed for that class interval.
* In histogram, the minimum and maximum value of interval of bar is called measurement of bars. Frequency density = Frequency of each class (bar)/Number of units of class interval
(b) Frequency Polygon
A frequency polygon shows a frequency distribution emphasizing the overall pattern in the data.
In this polygon fragmented categories are denoted an -Y-axis and frequencies are denoted on y-axis.
A frequency polygon can be constructed by two methods i.e., with the help of a histogram and without help of histogram.
I. Constructions of a Frequency Polygon with the help of Histogram
The frequency polygon is that type of polygon in which a closed two-dimensional figure of straight line segments joining the mid-points of the top of the bars of a histogram. The first point is located on the x-axis and is placed in the middle of the interval which precedes the first bar of the histogram.
The last point is located on the x-axis in the middle of the interval immediately following the last bar of the histogram.
Direction (Example 9) Draw a frequency polygon with the given data.
II. Construction of a F