In the NCERT Class 6 Maths Chapter 9 of Data Handling, we have briefly learned how to collect data, tabulate it and then represent it in the form of bar graphs. This form of collection, interpretation and representation of data helps us in better understanding of the data and to bring out useful results from them. In NCERT Class 7 Maths Chapter 3, Data Handling, we will study a step ahead of the previous data collection and handling. In this chapter, students will come across more types of data and their presentations. Let us now have a look at the NCERT Class 7 Maths Chapter 3 Data Handling Notes and Solutions (PDF).

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## NCERT Class 7 Maths Chapter 3 Notes – PDF Available

Check the topic-wise notes for NCERT Maths Class 7 – Chapter 3 below. You can also download the PDF of the notes and take a printout to study later when you need quick revision before going to the exam hall.

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### Topic 1: Collecting and Organising Data

Let us see the term that is used often in data collection and organisation below.

**Average:**An average is a number that represents or shows the central tendency of a group of observations or data.

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### Topic 2: Arithmetic Mean (AM)

The most common representative value of a group of data is the arithmetic mean or the mean.

The average or Arithmetic Mean (A.M.) or simply mean is calculated by:

### Topic 3: Range

The difference between the highest and the lowest observation gives us an idea of the spread of the observations. We call the result of this difference the range of the observation.

### Topic 4: Mode

It must be noted that the Mean is not the only measure of central tendency or the only form of

representative value. For different requirements from data, other measures of central tendencies are used.

**Mode:**The mode of a set of observations is the observation that occurs most often.

For example, in the data – 1, 1, 1, 2, 2, 2, 2, 3, 4, 4, “2” occurs the most number of times. So, 2 is the mode of the given observations.

We have seen how to determine the mode of a short set of data. This form of determining the mode of the given data is not feasible with the large set of data. Now, let us see how we can determine the mode for large data.

**Mode for Larger Data:**In case of larger data, we tabulate the data. Tabulation can begin by putting tally marks and finding the frequency.

### Topic 5: Median

Until now, we have seen that in some situations, the arithmetic mean is an appropriate measure of central tendency whereas, in some other situations, mode is the appropriate measure of central tendency.

The median helps to determine the middle of the data when the data set is arranged either in increasing or decreasing values. Thus we say that the median refers to the value which lies in the middle of the data (when arranged in an increasing or decreasing order) with half of the observations above it and the other half below it.

Thus, in a given data, arranged in ascending or descending order, the median gives us the middle observation.

For n number of values:

Median = (n/2)^{th} term, if n is even

And, Median = ½ × (n + 1)^{th} term, if n is odd

### Topic 6: Chance

There are situations in our life, that are certain to happen, some that are impossible and some that may or may not happen. The situation that may or may not happen has a chance of happening.

### Topic 7: Probability

Probability is the possibility of an event to happen. Events that have many possibilities can have a probability between 0 and 1. Those which have no chance of happening have probability 0 and those that are bound to happen have probability 1.

The formula for probability is:

## NCERT Class 7 Maths Chapter 3, Data Handling Solutions- Free PDF Download

Below we have provided solutions for NCERT Class 7 Maths Chapter 3, Data Handling. Go through for answers to some important questions.

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### Exercise 3.1 Solutions

**Q 1. Organise the following marks in a class assessment, in a tabular form.**

**4, 6, 7, 5, 3, 5, 4, 5, 2, 6, 2, 5, 1, 9, 6, 5, 8, 4, 6, 7**

**Which number is the highest?****Which number is the lowest?****What is the range of the data?****Find the arithmetic mean.**

**Solutions.** Let us tabulate the given data below.

Marks |
Tally Marks |
Frequency |

1 | I | 1 |

2 | II | 2 |

3 | I | 1 |

4 | III | 3 |

5 | 5 | |

6 | IIII | 4 |

7 | II | 2 |

8 | I | 1 |

9 | I | 1 |

- From the table, it is clear that the highest number is 9.
- The lowest number is 1.
- The range of data can be determined by subtracting the lowest value from the highest value.

Range = Highest Value – Lowest Value

∴ Range = 9 – 1 = 8

- We know that:

∴ Arithmetic Mean = 100/20 = 5

**Q 2. A cricketer scores the following runs in eight innings:**

**58, 76, 40, 35, 46, 45, 0, 100.**

**Find the mean score.**

**Solutions.** The mean scores can be calculated by:

So, the mean score of the cricketer is 50.

### Exercise 3.2 Solutions

**Q 1. The scores in mathematics test (out of 25) of 15 students are as follows:**

**19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, 20**

**Find the mode and median of this data. Are they the same?**

**Solutions. **We know that the most frequent value in a set of observations is the mode of the given data set. From the given test scores, it is clear that “20” is the mode of the given data of test scores.

Now, to determine the median, let us arrange the given test scores in increasing order below.

5, 9, 10, 12, 15, 16, 19, 20, 20, 20, 20, 23, 24, 25, 25

Now, the median of this organised data is the middle value of the data.

We have scores of 15 students, i.e. the total number of test scores is 15, which is odd.

n = 15

Median for odd number of observations = ½ × (n + 1)^{th} term = ½ × (15 + 1)^{th} term

The median of the given test scores = 8^{th } term

∴ the median of the given test scores is 20.

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**Q 2. The runs scored in a cricket match by 11 players are as follows:**

**6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15**

**Find the mean, mode and median of this data. Are the three the same?**

**Solutions.** The mean of the given scores can be calculated as:

Thus, **mean = 39**.

The mode of a given data is the most frequent value in the data set. By observing the given set of runs, it is clear that the **mode of the given data is 15**.

Now, to determine the median, let us arrange the given data in increasing order of their values.

6, 8, 10, 10, 15, 15, 15, 50, 80, 100, 120

We have runs scored by 11 cricketers, which is an odd number, i.e. n = 11.

Median for odd number of observations = ½ × (n + 1)^{th} term = ½ × (11 + 1)^{th} term

The median of the given test scores = 6^{th } term

∴ **median = 15**.

### Exercise 3.3 Solutions

**Q 1. Consider this data collected from a survey of a colony.**

Favourite Sport |
Cricket |
Basketball |
Swimming |
Hockey |
Athletics |

Watching |
1240 | 470 | 510 | 430 | 250 |

Participating |
620 | 320 | 320 | 250 | 105 |

**Draw a double bar graph choosing an appropriate scale. What do you infer from the bar graph?****Which sport is most popular?****Which is more preferred, watching or participating in sports?**

**Solutions. **The answers to each question are given below.

- The double bar graph for the given data is given below.

- From observing the bar graph above, it is clear that most people like to watch and participate in cricket. So, cricket is the most popular sport.
- Again, from the double bar graph above, it is clear that people prefer watching sports over participating.

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### Exercise 3.4 Solutions

**Q 1. Tell whether the following is certain to happen, impossible, can happen but not certain.**

**You are older today than yesterday.****A tossed coin will land heads up.****A dice when tossed shall land up with 8 on top.****The next traffic light seen will be green.****Tomorrow will be a cloudy day.**

**Solutions: **The answers are given below.

- It is a fact that you are older today than yesterday. So, this is certain to happen.
- Given the two sides of a coin, there are 50-50% chances of landing a heads or a tails. So, the event of landing of a tossed coin into heads can happen but is not certain.
- There are only 6 faces on a dice, numbered from 1 to 6. So, landing a dice with an 8 on top is impossible.
- Again, just like (b), this event can happen but is not certain.
- This event can happen but not certain.

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**Q 2. There are 6 marbles in a box with numbers from 1 to 6 marked on each of them.**

**What is the probability of drawing a marble with number 2?****What is the probability of drawing a marble with the number 5?**

**Solutions: **The answers are given below.

- Here the favourable outcome is – drawing a marble with the number 2 while the total number of outcomes is 6 (as there are 6 marbles numbered from 1 to 6). We know that probability can be calculated by:

∴ Probability of drawing a marble with the number 2 on it:

The probability is ⅙.

- As there is only 1 marble numbered 5, the probability of drawing a marble with the number 5 is:

The probability is ⅙.

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Check out Maths Class 6 Notes and Exercise Solutions for other chapters below.

## FAQs

**Q.1. What is Arithmetic Mean (AM)?**

Ans: The most common representative value of a group of data is the arithmetic mean or the mean. The average or Arithmetic Mean (A.M.) or simply mean is calculated by dividing the sum of all observations by the total number of observations.

**Q.2. What is Range, Class 7 Data Handling?**

Ans: The difference between the highest and the lowest observation gives us an idea of the spread of the observations. We call the result of this difference the range of the observation.

**Q.3. What is the Mode of a data set?**

Ans: The mode of a set of observations is the observation that occurs most often.

For example, in the data – 1, 1, 1, 2, 2, 2, 2, 3, 4, 4, “2” occurs the most number of times. So, 2 is the mode of the given observations.

This was all about NCERT Class 7 Maths Chapter 3, Data Handling in which we studied the different properties of integers. Download the NCERT Class 7 Maths Chapter 3 Notes and Solutions PDF to ace your exam preparations. Follow the **CBSE Class 7 Maths Solutions and Notes** for more such chapter notes and important questions and answers for preparation for CBSE Class 7 Maths.