Graphs

## Introduction

Have you seen graphs in the newspapers, television, magazines, books etc.? The purpose of the graph is to show numerical facts in visual form so that they can be understood quickly, easily and clearly. Thus graphs are visual representations of data collected. Data can also be presented in the form of a table; however a graphical presentation is easier to understand. This is true in particular when there is a trend or comparison to be shown. We have already seen some types of graphs. Let us quickly recall them here.

## A Bar graph

A bar graph is used to show comparison among categories. It may consist of two or more parallel vertical (or horizontal) bars (rectangles).

The bar graph in Fig 15.1 shows Anu’s mathematics marks in the three terminal examinations. It helps you to compare her performance easily. She has shown good progress.

Bar graphs can also have double bars as in Fig 15.2. This graph gives a comparative account of sales (in Rs) of various fruits over a two-day period. How is Fig 15.2 different from Fig 15.1? Discuss with your friends

## A Pie graph (or a circle-graph)

A pie-graph is used to compare parts of a whole. The circle represents the whole. Fig 15.3 is a pie-graph. It shows the percentage of viewers watching different types of TV channels.

## A histogram

A Histogram is a bar graph that shows data in intervals. It has adjacent bars over the intervals. The histogram in Fig 15.4 illustrates the distribution of weights (in kg) of 40 persons of a locality.

There are no gaps between bars, because there are no gaps between the intervals. What is the information that you gather from this histogram? Try to list them out.

## A line graph

A line graph displays data that changes continuously over periods of time.
When Renu fell sick, her doctor maintained a record of her body temperature, taken every four hours. It was in the form of a graph (shown in Fig 15.5 and Fig 15.6).
We may call this a “time-temperature graph”.
It is a pictorial representation of the following data, given in tabular form.

 Time 6am 10am 2pm 6pm Temperature(°C) 37 40 38 35

The horizontal line (usually called the x-axis) shows the timings at which the temperatures were recorded. What are labelled on the vertical line (usually called the y-axis)?

What all does this graph tell you? For example you can see the pattern of temperature; more at 10 a.m. (see Fig 15.5) and then decreasing till 6 p.m. Notice that the temperature increased by 3° C(= 40° C – 37° C) during the period 6 a.m. to 10 a.m. There was no recording of temperature at 8 a.m., however the graph suggests that it was more than 37 °C (How?).

Example 1: (A graph on “performance”) The given graph (Fig 15.7) represents the total runs scored by two batsmen A and B,
during each of the ten different matches in the year 2007. Study the graph and answer the following questions.
(i) What information is given on the two axes?
(ii) Which line shows the runs scored by batsman A?
(iii) Were the run scored by them same in any match in 2007? If so, in which match?
(iii) Among the two batsmen, who is steadier? How do you judge it?

Solution:
(i) The horizontal axis (or the x-axis) indicates the matches played during the year 2007. The vertical axis (or the y-axis) shows the total runs scored in each match.
(ii) The dotted line shows the runs scored by Batsman A. (This is already indicated at the top of the graph).

(iii) During the 4th match, both have scored the same number of 60 runs. (This is indicated by the point at which both graphs meet).
(iv) Batsman A has one great “peak” but many deep “valleys”. He does not appear to be consistent. B, on the other hand has never scored below a total of 40 runs, even though his highest score is only 100 in comparison to 115 of A. Also A has scored a zero in two matches and in a total of 5 matches he has scored less than 40 runs. Since A has a lot of ups and downs, B is a more consistent and reliable batsman.

Example 2: The given graph (Fig 15.8) describes the distances of a car from a city P at different timeswhen it is travelling from City P to City Q, which are 350 km apart. Study the graph and answer the following:

(i) What information is given on the two axes?

(ii) From where and when did the car begin its journey?

(iii) How far did the car go in the first hour?

(iv) How far did the car go during (i) the 2nd hour? (ii) the 3rd hour?

(v) Was the speed same during the first three hours? How do you know it?

(vi) Did the car stop for some duration at any place? Justify your answer.

(vii) When did the car reach City Q?

Solution:

(i) The horizontal (x) axis shows the time. The vertical (y) axis shows the distance of the car from City P.

(ii) The car started from City P at 8 a.m.

(iii) The car travelled 50 km during the first hour. [This can be seen as follows.  At 8 a.m. it just started from City P. At 9 a.m. it         was at the 50th km (seen from graph). Hence during the one-hour time between 8 a.m. and 9 a.m. the car travelled 50 km].

(iv) The distance covered by the car during

(a) the 2nd hour (i.e., from 9 am to 10 am) is 100 km, (150 – 50).

(b) the 3rd hour (i.e., from 10 am to 11 am) is 50 km (200 – 150).

(v) From the answers to questions (iii) and (iv), we find that the speed of the car was not the same all the time. (In fact the graph  illustrates how the speed varied).

(vi) We find that the car was 200 km away from city P when the time was 11 a.m. and also at 12 noon. This shows that the car did not travel during the interval 11 a.m. to 12 noon. The horizontal line segment representing “travel” during this period is illustrative of this fact.

(vii) The car reached City Q at 2 p.m.

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