CBSE Class 7 Mathematics Data Handling Notes

CBSE Class 6 English Practice Passages. Learning the important concepts is very important for every student to get better marks in examinations. The concepts should be clear which will help in faster learning. The attached concepts made as per NCERT and CBSE pattern will help the student to understand the chapter and score better marks in the examinations.

Data Handling

Data Representation

Any information collected can be first arranged in a frequency distribution table, and this information can be put as a visual representation in the form of pictographs or bar graphs. Graphs are a visual representation of organised data.

A bar graph is the representation of data using rectangular bars of uniform width, and with their lengths depending on the frequency and the scale chosen. The bars can be plotted vertically or horizontally. You can look at a bar graph and make deductions about the data.

Bar graphs are used for plotting discrete or discontinuous data, i.e. data that has discrete values and is not continuous. Some examples of discontinuous data are 'shoe size' and 'eye colour', for which you can use a bar chart. On the other hand, examples of continuous data include 'height' and 'weight'. A bar graph is very useful if you are trying to record certain information, whether the data is continuous or not.

Graphs can also be used for comparative analysis. Double bar graphs are used for comparing data between two different things. The difference between a bar graph and a double bar graph is that a bar graph displays one set of data, and a double bar graph compares two different sets of information or data.

Example 1: Draw simple bar diagram to represent the profits of a bank for 5 years.

Example 2:      Draw multiple bar chart to represent the import and export of Canada (values in $) for the years 1991 to 1995.

Measure of Central tendency

1.Arithmetic mean: Arithmetic mean is a number that lies between the highest and the lowest value of data.   

Note: Arranging the data in ascending or descending order is not needed to calculate arithmetic mean.

2.Range: Range = Highest observation – Lowest observation 

3.Mode: Mode refers to the observation that occurs most often in a given data. The following are the steps to calculate mode:

Step – 1: Arrange the data in ascending order

Step – 2: Tabulate the data in a frequency distribution table.

Step – 3: The most frequently occurring observation will be the mode.

Note:

• It is possible for a set of data values to have more than one mode.

• If there are two data values that occur most frequently, we say that the set of data values is bimodal.

• If there is no data value or data values that occur most frequently, we say that the set of data values has no mode.

4. Median: Median refers to the value that lies in the middle of the data with half of the observations above it and the other half of the observations below The following are the steps to calculate median

Step – 1: Arrange the data in ascending order.

Step – 2: Find the middle terms.

If there is only one middle term, then that term is the median. If there are two middle terms, then the average of both the terms gives the median.

The mean, mode and median are representative values of a group of observations or data, and lie between the minimum and maximum values of the data. They are also called measures of the central tendency.

Example: Calculate the arithmetic mean, range, median and mode of the following data:

2, 4, 7, 4, 9, 5, 7, 3, 6, 7

Solution:

Arithmetic mean = sum of all observations / number of observations = 2 + 4 + 7 + 4 + 9 + 5 + 7 + 3 + 6 + 7 / 10

Median: 54/10 = 5 . 4

Step –I : Arranging the datas in ascending order,

2,3,4,4,5,6,7,7,7,9

Step –II Here the middle terms are 5 and 6

The average of 5 and 6 = 5 + 6 / 2 = 11/2 = 5.5

Therefore, Median = 5.5

Mode: The most repeating values is 7. Therefore, Mode is 7.

Range: Range = Highest observation – Lowest observation = 9 – 2 =7

Mode of Large Data

Example: Following are the margins of victory in the football matches of a league.

1, 3, 2, 5, 1, 4, 6, 2, 5, 2, 2, 2, 4, 1, 2, 3, 1, 1, 2, 3, 2,6, 4, 3, 2, 1, 1, 4, 2, 1, 5, 3, 3, 2, 3, 2, 4, 2, 1, 2

Find the mode of this data.

Solution: Let us put the data in a tabular form:

Since 2 has occurred the highest number of times 2 is the mode. Thus, most of the matches have been won with a victory margin of 2 goals.

Probability

In our daily life we come across the words like probably, likely, may be, chance and hope etc. All these are synonyms to probability.

Probability is defined as the numerical method of measuring uncertainty involved in a situation.

It is widely used in the study of mathematics, statistics, gambling, physical science, biological science, weather forecasting, finance etc. to draw conclusions. An experiment is defined as an action or process that results in well defined outcomes.

An experiment, in which we know all the results, but cannot predict them, is called a random experiment. The possible results of an experiment are called the outcomes A combination of outcomes is called an event. For example when an unbiased die is rolled getting an even number is an event. In this event the outcomes are {2,4,6}. When an experiment is performed, outcomes are said to be equally likely, if each outcome has the same chance of occurring. Probability of event E is defined as :

Probability of event = No. of favourable outcomes / Total number of outcomes

Examples: A bag has 4 red balls and 2 yellow balls. (The balls are identical in all respects other than colour). A ball is drawn from the bag without looking into the bag. What is probability of getting a red ball? Is it more or less than getting a yellow ball?

Solution: There are in all (4 + 2 =) 6 outcomes of the event.

Getting a red ball consists of 4 outcomes.

Probability of event = No . of favourable outcomes / Total number of outcomes

Therefore, i) the probability of getting a red ball = 4/6 = 3/2

ii) the probability of getting a yellow ball = 2/6 = 2/3

Therefore, the probability of getting a red ball is more than that of getting a yellow ball.

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