CBSE Notes Class 7 Maths Chapter 3 Data Handling

CBSE Class 7 Maths Chapter 3: Data Handling focuses on the collection, organization, and interpretation of data to draw meaningful conclusions. This chapter is essential for making informed decisions and understanding patterns in various contexts. Students will explore different methods of representing data, including graphs and charts, while also learning how to calculate key measures such as mean, median, and mode. Mastering data handling equips students with vital skills for analyzing information in real-life situations.

1.0Data 

The word data means information in the form of numerical figures or a set of given facts. E.g. The percentage of marks scored by 10 students of a class in a test are 72, 84, 82, 96, 94, 98, 99, 67, 92 and 93

2.0Some Basic Definitions

1. Raw data: 

Data obtained from direct observation is called raw data. The marks obtained by 10 students in a monthly test are an example of raw data or ungrouped data. 

2. Observation: Each numerical figure in the set of data is called an observation. 
3. Array: Arranging the numerical figures of a set of data in ascending order is called an array. 
4. Range: The difference between the highest and lowest values of the observation in a given set of data is called its range. 
5. Frequency: 

The frequency of an observation refers to the number of times it appears. 

The collection of a particular type of information in the form of numerical figures is called, a set of data. 

This set of data obtained in the original form is called a set of raw (or ungrouped) data. 

6. Frequency distribution: 

The number of times a particular observation occurs is called its frequency. 

The table showing the frequencies of various observations of data is called a frequency distribution table or simply frequency table. 

We take each observation from the data and count them with the help of strokes called tally marks. For the sake of convenience, we use tally marks in bunches of five, i.e. the fifth one crossing the four diagonally.

7. Tabulation or presentation of data: A systematic arrangement of data in a tabular form is called tabulation or presentation of the data.

3.0Arithmetic mean 

The arithmetic mean in statistics is the same as 'average' in arithmetic. 

1. Mean of ungrouped or raw data 

The mean of a set of data is found out by dividing the total sum of all the observations by the total number of observations in the data. We denote the mean by x (read 'x bar').

$Mean=\bar{X}=\frac{SumofObservations}{NumberofObservations}$

2. Median 

The median of a set of numbers is the middle number when all the numbers are arranged in order of size, i.e., in descending or ascending order. 

Method for finding the median of an ungrouped data 

To determine the median of a dataset, arrange the numbers in either increasing or decreasing order. Let the total no of observations be n.  

Case 1: When n is odd, the median is the value of the $(\frac{n+1}{2}{)}^{th}$  observation.  

Case 2: When n is even, the median is the mean of the two middle values.

$Median=\frac{1}{2}[(\frac{n}{2}{)}^{th}observation+(\frac{n}{2}+1{)}^{th}observation]$

3. Mode of ungrouped data 

The mode of a set of numbers is the number which occurs most frequently in the set. If no numbers occur more than once, the set of data is said to have no mode. For example, in the following set of data 3, 6, 9, 16, 27, 37, 48, no number appears more than once. Hence there is no mode available. If different numbers occur the same number of times, the set of data has more than one mode. 

Note: For finding mean and mode, it is not necessary to arrange the given set of data in an ascending or descending order.

Empirical formula for calculating mode 

We use the formula 

Mode = 3(Median) – 2(Mean)

4.0Statistical Graphs 

There are different types of graphs or diagrams to represent statistical data. Some of them are 

1. Pictograph 
2. Bar graph 
3. Double bar graph 

Pictograph 

It is a pictorial/visual representation of data using symbols. By observing the pictograph one can easily understand the given data. 

we take a convenient scale to draw a pictograph for the above data.

Bar graph 

A bar graph displays numerical data using bars of equal width, with heights proportional to the values they represent. The bars reflect the values they represent and can be drawn either vertically or horizontally.

Example: Represent the given data on a bar graph.

Double bar graph 

A double or dual bar graph helps you to make comparisons between two related pieces of data at the same time

Example: Represent the given data on a bar graph.

5.0Probability

1. Chance Factor: In daily life, we encounter events that are possible but uncertain, like winning a card game—there's a chance, but no certainty.
2. Equally Likely Outcomes:

(i) Tossing a coin gives equal chances of landing on heads or tails.  

(ii) In cricket, both teams have an equal chance of winning, especially in a match between two strong teams.

3. Unlikely Outcomes: Buying a lottery ticket gives you a very low chance of winning since millions participate. Similarly, while it's likely Ravi will be promoted, it’s unlikely Rekha will achieve the top position in class.
4. More Likely Outcomes: In a basket with 16 apples and 8 bananas, if Sangita picks one without looking, she is more likely to select an apple.

Empirical Probability

Empirical probability measures the chance of an outcome using numbers. If we conduct n trials of an experiment, the probability of an event E occurring is defined as:

$P(E)=\frac{NumberoftrialsinwhichEoccurs}{Totalnumberoftrials}$

6.0Mind Maps for Data Handling