Data Handling

9.1 Introduction

In your day to day life, you must have seen several kinds of tables consisting of numbers, figures, names etc. These tables provide ‘Data’. A data is a collection of numbers gathered to give some information.

9.2 Recording Data

Let us take an example of a class which is preparing to go for a picnic.

The teacher asked the students to give their choice of fruits out of banana, apple, orange or guava.

Uma is asked to prepare the list. She prepared a list of all the children and wrote the choice of fruit against each name.

This list would help the teacher to distribute fruits according to the choice.

If the teacher wants to know the number of bananas required for the class, she has to read the names in the list one by one and count the total number of bananas required.

To know the number of apples, guavas and oranges separately she has to repeat the same process for each of these fruits. How tedious and time consuming it is!

It might become more tedious if the list has, say, 50 students.

· So, Uma writes only the names of these fruits one by one like, banana, apple, guava, orange, apple, banana, orange, guava, banana, banana, apple, banana, apple, banana, orange, guava, apple, banana, guava, and banana.

Do you think this makes the teacher’s work easier?

· She still has to count the fruits in the list one by one as she did earlier.

· Salma has another idea.

· She makes four squares on the floor. Every square is kept for fruit of one kind only.

· She asks the students to put one pebble in the square which matches their choices.

· i.e. a student opting for banana will put a pebble in the square marked for banana and so on. By counting the pebbles in each square, Salma can quickly tell the number of each kind of fruit required.

· She can get the required information quickly by systematically placing the pebbles in different squares

9.3 Organization of Data

To get the same information which Salma got, Ronald needs only a pen and a paper. He does not need pebbles. He also does not ask students to come and place the pebbles. He prepares the following table

What does one (✓) mark indicate? Four students preferred guava.

How many (✓) marks are there against guava? How many students were there in the class? Find all this information. Discuss about these methods. Which is the best? Why? Which method is more useful when information from a much larger data is required?

Example 1:

A teacher wants to know the choice of food of each student as part of the mid-day meal program. The teacher assigns the task of collecting this information to Maria. Maria does so using a paper and a pencil. After arranging the choices in a column, she puts against a choice of food one ( | ) mark for every student making that choice.

Umesh, after seeing the table suggested a better method to count the students. He asked Maria to organize the marks ( | ) in a group of ten as shown below :

Rajan made it simpler by asking her to make groups of five instead of ten, as shown below:

Teacher suggested that the fifth mark in a group of five marks should be used as a cross, as shown by ‘ ’. These are tally marks. Thus, shows the count to be five plus two (i.e. seven) and shows five plus five (i.e. ten). With this, the table looks like:

Example 2: Ekta is asked to collect data for size of shoes of students in her Class VI. Her finding are recorded in the manner shown below :

Javed wanted to know

(i) The size of shoes worn by the maximum number of students.

(ii) The size of shoes worn by the minimum number of students. Can you find this information?

Ekta prepared a table using tally marks.

9.4 Pictograph

A cupboard has five compartments. In each compartment a row of books is arranged. The details are indicated in the adjoining table:

Which row has the greatest number of books? Which row has the least number of books? Is there any row which does not have books?

You can answer these questions by just studying the diagram. The picture visually helps you to understand the data. It is a pictograph.

● A pictograph represents data through pictures of objects. It helps answer the questions on the data at a glance.

9.5 Interpretation of a Pictograph

Example 3: The following pictograph shows the number of absentees in a class of 30 students during the previous week :

(a) On which day were the maximum number of students absent?

(b) Which day had full attendance?

Solution:

(a) Maximum absentees were on Saturday. (There are 8 pictures in the row for Saturday; on all other days, the number of pictures are less).

(b) Against Thursday, there is no picture, i.e. no one is absent. Thus, on that day the class had full attendance.

Example 4: The colours of fridges preferred by people living in a locality are shown by the following pictograph:

(a) Find the number of people preferring blue colour.

(b) How many people liked red colour?

Solution:

(a) Blue colour is preferred by 50 people. [= 10, so 5 pictures indicate 5 × 10 people].

(b) Deciding the number of people liking red colour needs more care.

For 5 complete pictures, we get 5 × 10 = 50 people.

For the last incomplete picture, we may roughly take it as 5.

So, number of people preferring red colour is nearly 55.

Example 5:

A survey was carried out on 30 students of class VI in a school. Data about the different modes of transport used by them to travel to school was displayed as pictograph. What can you conclude from the pictograph?

Solution:

From the pictograph we find that:

(a) The number of students coming by private car is 4.

(b) Maximum number of students use the school bus. This is the most popular way.

(d) The number of students using the other modes can be similarly found.

Example 6: Following is the pictograph of the number of wrist watches manufactured by a factory in a particular week.

(a) On which day were the least number of wrist watches manufactured?

(b) On which day were the maximum number of wrist watches manufactured?

Solution:

We can complete the following table and find the answers.

9.6 Drawing a Pictograph

Example 7: The following are the details of number of students present in a class of 30 during a week. Represent it by a pictograph.

Solution:

With the assumptions we have made earlier,

24 may be represented by

26 may be represented by and so on. Thus, the pictograph would be

We had some sort of agreement over how to represent ‘less than 5’ by a picture. Such a sort of splitting the pictures may not be always possible. In such cases what shall we do? Study the following example.

Example 8: The following are the number of electric bulbs purchased for a lodging house during the first four months of a year.

Represent the details by a pictograph.

Solution:

Picturising for January and March is not difficult. But representing 26 and 34 with the pictures is not easy.

We may round off 26 to nearest 5 i.e. to 25 and 34 to 35. We then show two and a half bulbs for February and three and a half for April.

9.7 A Bar Graph

Representing data by pictograph is not only time consuming but at times difficult too. Let us see some other way of representing data visually. Bars of uniform width can be drawn horizontally or vertically with equal spacing between them and then the length of each bar represents the given number. Such method of representing data is called a bar diagram or a bar graph

9.7.1 Interpretation of a bar graph

Let us look at the example of vehicular traffic at a busy road crossing in Delhi, which was studied by the traffic police on a particular day. The number of vehicles passing through the crossing every hour from 6 a.m. to 12.00 noon is shown in the bar graph. One unit of length stands for 100 vehicles.

· We can see that maximum traffic is shown by the longest bar (i.e. 1200 vehicles) for the time interval 7-8 a.m. The second longer bar is for 8-9 a.m. Similarly, minimum traffic is shown by the smallest bar (i.e. 100 vehicles) for the time interval 6-7 a.m. The bar just longer than the smallest bar is between 11 a.m. - 12 noon.

· The total traffic during the two peak hours (8.00-10.00 am) as shown by the two long bars is 1000+900 = 1900 vehicles.

· If the numbers in the data are large, then you may need a different scale. For example, take the case of the growth of the population of India. The numbers are in cores.

· So, if you take 1 unit length to be one person, drawing the bars will not be possible. Therefore, choose the scale as 1 unit to represents 10 crores.

· The bar graph for this case is shown in the figure. So, the bar of length 5 units represents 50 crores and of 8 units represents 80 crores.

Example 9:

Read the adjoining bar graph showing the number of students in a particular class of a school. Answer the following questions:

(a) What is the scale of this graph?

(b) How many new students are added every year?

Solution:

(a) The scale is 1 unit length equals 10 students.

Try (b) and (c) for yourself.

9.7.2 Drawing a bar graph

Recall the example where Ronald (section 9.3) had prepared a table representing choice of fruits made by his classmates. Let us draw a bar graph for this data.

First of all draw a horizontal line and a vertical line.

On the horizontal line we will draw bars representing each fruit and on vertical line we will write numerals representing number of students.

Let us choose a scale. It means we first decide how many students will be represented by unit length of a bar.

Here, we take 1 unit length to represent 1 student only.

We get a bar graph as shown in adjoining figure.

Example 10: Following table shows the monthly expenditure of Imran’s family on various items

To represent this data in the form of a bar diagram, here are the steps.

(a) Draw two perpendicular lines, one vertical and one horizontal.

(b) Along the horizontal line, mark the ‘items’ and along the vertical line, mark the corresponding expenditure.

(d) Choose suitable scale along the vertical line.

Let 1 unit length = ` 200 and then mark the corresponding values. Calculate the heights of the bars for various items as shown below.

House rent: 3000 ÷ 200 = 15 units

Food: 3400 ÷ 200 = 17 units

Education: 800 ÷ 200 = 4 units

Electricity: 400 ÷ 200 = 2 units

Transport: 600 ÷ 200 = 3 units

Miscellaneous: 1200 ÷ 200 = 6 units

Same data can be represented by interchanging positions of items and expenditure as shown below: