Class 7 — Mathematics (NCERT)
Data Handling
Class 7
- ✓By the end of this lesson students will be able to understand what data is and how to organise it.
- ✓By the end of this lesson students will be able to calculate the arithmetic mean, median, mode, and range of a given data set.
- ✓By the end of this lesson students will be able to draw and interpret bar graphs and double bar graphs.
- ✓By the end of this lesson students will be able to understand the concepts of chance and probability.
- ✓By the end of this lesson students will be able to calculate the probability of simple events.
Key concepts
Data is a collection of numerical facts or figures gathered to give some information. For example, marks obtained by students in a test, number of absentees in a class, or heights of students.
Data collected in its original form, without any organisation or processing, is called raw data.
To make data understandable and easy to interpret, it needs to be organised. This can be done using frequency distribution tables, often involving tally marks.\n* Tally Marks: A system of counting where each occurrence is represented by a vertical line, and every fifth line is drawn diagonally across the previous four.\n* Frequency: The number of times a particular observation occurs in a data set.
The Arithmetic Mean (or simply Mean) is the most common representative value of a group of data. It is calculated by dividing the sum of all observations by the total number of observations. It is often referred to as the average.
The range of a data set is the difference between the highest and the lowest observation in the data. It gives an idea of the spread of the data.
The median is the middle value of a data set when the data is arranged in ascending or descending order.\n* If the number of observations (n) is odd, the median is the ((n+1)/2)th observation.\n* If the number of observations (n) is even, the median is the average of the (n/2)th and ((n/2)+1)th observations.
The mode is the observation that occurs most frequently in a data set. A data set can have one mode, more than one mode (multimodal), or no mode at all.
A bar graph is a pictorial representation of data using bars of uniform width drawn vertically or horizontally with equal spacing between them. The length of each bar represents the frequency of the corresponding observation.
A double bar graph is used to compare two sets of data simultaneously. For example, comparing the performance of a class in two different tests or comparing sales of two different products over time.
Many events in our daily life involve an element of chance. Probability is a measure of the likelihood that an event will occur.\n* Random Experiment: An experiment whose outcome cannot be predicted with certainty, but all possible outcomes are known (e.g., tossing a coin, rolling a die).\n* Outcome: A possible result of a random experiment.\n* Event: One or more outcomes of an experiment.\n* Equally Likely Outcomes: Outcomes that have the same chance of occurring.
Key facts to remember
- 1Data is a collection of numerical facts gathered to give information.
- 2The Arithmetic Mean is the sum of observations divided by the number of observations.
- 3The Range is the difference between the highest and lowest observations.
- 4The Median is the middle value of the data when arranged in order.
- 5The Mode is the observation that occurs most frequently.
- 6A bar graph uses bars to represent data, and a double bar graph compares two sets of data.
- 7Probability measures the chance of an event occurring: P(Event) = (Favourable Outcomes) / (Total Outcomes).
- 8The probability of any event always lies between 0 and 1, inclusive.
Worked examples
Example 1
The marks obtained by 10 students in a mathematics test (out of 50) are given below:\n42, 35, 48, 20, 39, 42, 25, 30, 42, 32.\nFind the mean, median, mode, and range of this data.
Answer
Range = 28, Mean = 35.5, Median = 37, Mode = 42
Always arrange the data in ascending or descending order before finding the median.
Example 2
The following double bar graph shows the number of students in Class 7 who prefer different subjects in two different schools, School A and School B.\nSubject | School A | School B\n--------|----------|---------\nMaths | 40 | 50\nScience | 35 | 30\nEnglish | 25 | 45\nSocial | 30 | 20\nAnswer the following questions:\n(a) Which subject is most preferred in School A?\n(b) Which subject is least preferred in School B?\n(c) What is the total number of students who prefer Maths in both schools?
Answer
(a) Maths, (b) Social, (c) 90 students
Always read the labels and scale carefully when interpreting bar graphs.
Example 3
A bag contains 3 red balls and 5 blue balls. A ball is drawn at random from the bag. What is the probability of drawing:\n(a) a red ball?\n(b) a blue ball?\n(c) a green ball?
Answer
(a) P(Red ball) = 3/8, (b) P(Blue ball) = 5/8, (c) P(Green ball) = 0
The probability of an impossible event is 0, and the probability of a sure event is 1. Probability always lies between 0 and 1 (inclusive).
Common mistakes
- ✗Forgetting to arrange data in ascending/descending order before finding the median.
- ✗Confusing mean, median, and mode, or using the wrong formula for each.
- ✗Not labelling axes or providing a scale when drawing bar graphs.
- ✗Incorrectly counting total outcomes or favourable outcomes when calculating probability.
- ✗Stating probability as a number greater than 1 or less than 0.
Exam tips
- ★Read the question carefully to identify whether mean, median, or mode is required.
- ★Always show your working steps clearly, especially for calculations of mean, median, and probability.
- ★When drawing bar graphs, use a ruler and pencil, ensure uniform bar width, equal spacing, and proper labelling of axes and scale.
- ★For probability questions, list all possible outcomes and favourable outcomes to avoid errors.
- ★Double-check your calculations, especially for mean and median, to avoid arithmetic mistakes.
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