Data Handling Class 3 Notes Maths

Double Bar Graphs

Introduction:

Double bar graphs are like superhero tools for comparing two things at once. Imagine you have marks from two tests for five students. A double bar graph helps us see, at a glance, which week the students did better.

Key Points:

• Double bar graphs compare two quantities for the same observation.
• They are great for analyzing and comparing data effectively.

Averages

Introduction:

Averages help us find the typical value in a bunch of numbers. It's like finding the middle point. The range, on the other hand, tells us how spread out the numbers are.

Key Points:

• Mean (Average): Sum of all numbers divided by the count of numbers.
• Range: The difference between the highest and lowest numbers in a set.

Example:

Heights of all 10 basketball players are: 150 cm, 165 cm, 142 cm, 175 cm, 160 cm, 180 cm, 155 cm, 148 cm, 170 cm, 155 cm.

Mean height = (150 + 165 + 142 + 175 + 160 + 180 + 155 + 148 + 170 + 155) / 10 = 159.5 cm

Range = Highest Observation – Lowest Observation = 180 cm (highest) – 142 cm (lowest) = 38 cm

So, in this example, the mean height of the basketball players is 159.5 cm, and the range of their heights is 38 cm.

Median

Introduction:

Think of the median as the superstar in the middle when all your numbers are in a row. It's the middlemost friend in the group!

Key Points:

• Median is the middlemost value when data is arranged in order.
• It helps us understand the middle value of our numbers.

Example: 

Scores of all nine students are: 78, 92, 65, 87, 75, 94, 80, 68, 85.

Observations in ascending order: 65, 68, 75, 78, 80, 85, 87, 92, 94.

Since there are an odd number of observations (nine in this case), the median is the middlemost value, which is the fifth observation.

Median = 80

Therefore, the median score of the students in the math quiz is 80. The median gives us a central value that helps us understand the typical performance in the quiz.

Mode

Introduction:

Mode is like the popular kid in your class. It's the number that shows up the most, the real MVP!

Key Points:

• Mode is the number that occurs most frequently in a set.
• A set can have more than one mode.

Example:

Number of books read by ten students: 3, 2, 4, 2, 5, 3, 2, 4, 5, 4.

Arranging in ascending order: 2, 2, 2, 3, 3, 4, 4, 4, 5, 5.

In this case, the number "2" occurs most frequently. However, there is another number, "4," that also occurs the same number of times as the mode. Therefore, this data set has two modes: 2 and 4.

So, the modes of this data set are 2 and 4. This example illustrates that it's possible for a dataset to have more than one mode, making our exploration of data even more interesting!

Chance and Probability

Introduction:

Probability is like predicting the chances of something happening. It's like guessing which team might win in a game!

Key Points:

• Probability measures the chance of an event happening.
• The sample space is all the possible outcomes in an experiment.

Example: 

When a standard six-sided die is rolled, the sample space (S) is {1, 2, 3, 4, 5, 6}.

Favourable outcomes (even numbers in this case): {2, 4, 6}

The probability (P) of rolling an even number can be calculated using the formula:

P(even number)=Number of favourable outcomes/Total number of possible outcomes

P(even number)=3/6

Simplifying the fraction:

P(even number)=1/2

Therefore, the probability of rolling an even number on a standard six-sided die is 1221. This means that, on average, one out of every two rolls will result in an even number.

Recording Data using Tally Marks

Collection of information in the form of numerical figures is called data. To collect information or data, you conduct a survey by asking people a question and recording their answers. Let us conduct a survey.

Survey — Favourite Ice Cream

Ask other children of your neighbourhood their favourite ice cream.
Suppose you get the answers as:

With this information or data, if seen as such, it is not so easy to know at a glance, which ice cream was liked most or least?
This information needs to be presented in a tabular form, where the favourite ice cream as well as the number of children liking it is clear and easy to read.
Tally marks are an easy way to keep track of the data you collect in a survey.
You draw a vertical line for each answer conducted as:
To present information using tally marks, you can use a tally chart. 
The information you collected in the ice cream survey can be displayed on a tally chart as given on the next page.

As against the information collected in the survey, the tally chart given on the left shows the number of children against each ice cream clearly at a glance.

Pictographs

A pictograph is a type of graph that uses pictures or symbols to represent the data. It gives us precise, quick and exact information.

Reading and Drawing Pictographs

The following table shows the favourite fruits and the number of the children who like each fruit.

We can represent this information by a pictograph as shown:
Every pictograph has:

Study another illustration.
The following table shows the favourite subjects of the students of Class 3:

The pictograph for the above data is given below:
Favourite Subjects of the Students of Class 3