Class 9 Maths Chapter 14 Statistics

Statistics helps us make sense of large sets of data by presenting them in an organised form. It is widely used in everyday life, such as in surveys, reports, planning and decision-making. 

We provide well-structured and concise notes for all subjects, helping students revise effectively even when time is limited. In this chapter, we will share important notes for Class 9 Statistics along with solved examples. Let’s begin learning it in a step-by-step and well-organised manner.

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What is Statistics?

Statistics is the branch of knowledge that deals with the collection, organisation, presentation, analysis, and interpretation of numerical data. It helps in converting raw data into meaningful information for better understanding and decision-making.

In everyday life, statistics helps us to:

• Compare data (such as marks, income, population, etc.)
• Make predictions and forecasts
• Identify trends and patterns
• Support planning and policy decisions

Statistics is widely used in fields like economics, business, government planning, science, education, and research. It plays an important role in simplifying complex data and presenting it in a clear and systematic form through tables, graphs, averages, percentages, etc.

In short, statistics helps us understand facts and figures in a scientific and logical manner.

What is Data?

It refers to any small piece of information that is in the form of fact and figure. We use data to calculate something. 

1. Types of Data

There are two types of data:

• Primary data: It refers to the data collected by NGOs and official organizations in order to gain knowledge about some topic.
• Secondary data: It refers to the data collected by third-party organizations for their own personal purposes.

2. Presentation of Data 

After collecting data, it is often presented in a systematic manner so that all figures can be easily understood. There are different methods of presenting data depending on the size and nature of the information collected.

3. Ungrouped Data

When data is collected and presented without any further organisation or classification, it is called ungrouped data.

Example:

Marks obtained by students in a mathematics class test are: 90, 36, 22, 11, 10, 8, 2

Here, there is a large difference between the highest and lowest values. Since the data is not arranged into groups, it is known as ungrouped data.

4. Grouped Data

When data is organised into groups or class intervals to represent a large number of observations, it is called grouped data.

• Class Interval: The group used to classify the data
• Upper Class Limit: The highest value of a class interval
• Lower Class Limit: The lowest value of a class interval
• Class Size: Difference between the upper and lower class limits
• Class Mark: The mid-point of a class interval: Class mark = (Lower limit of the class + Upper limit of the class) ÷ 2

5. Frequency Distribution

When the number of observations is large, it becomes difficult to study individual values. In such cases, data is arranged in tabular form showing the number of times each observation occurs. This table is called a frequency distribution table.

Mean, Median and Mode

Measures of central tendency help us find a single value that represents the entire data. The three main measures are Mean, Median and Mode.

1. Mean

Mean refers to the average of all observations in a given data.

Formula:

Mean = (Sum of all observations) ÷ (Total number of observations)

2. Median

Median refers to the middle value of the data when it is arranged in ascending or descending order.

Steps to find Median:

1. Arrange the data in ascending order.
2. If the number of observations is odd, the middle value is the median.
3. If the number of observations is even, the median is the average of the two middle values.

3. Mode

Mode refers to the value that occurs most frequently in the given data.

Example: 2, 3, 3, 3, 3, 3, 5

Here, the number 3 occurs the maximum number of times, so the mode = 3.

NCERT Solutions for Class 9 Maths Ch-14 Statistics

Q1. Distance (in km) of 40 engineers from their place of residence to their place of work were found as follows :

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Construct a grouped frequency distribution table with class size 5 for the data given above taking the first interval as 0 – 5 (5 not included). What main features do you observe from this tabular representation?

Solution: The grouped frequency distribution table for the given data is as follows:

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From the table we observe that out of 40 female engineers 36 (5 +11 + 11 + 9) engineers i.e. 90% of the total female engineers reside less than 20 km from their place of work.

Q2. The relative humidity (in %) of a certain city for a month of 30 days was as follows :

98.1 98.6 99.2 90.3 86.5 95.3 92.9 96.3 94.2 95.1

89.2 92.3 97.1 93.5 92.7 95.1 97.2 93.3 95.2 97.3

96.2 92.1 84.9 90.2 95.7 98.3 97.3 96.1 92.1 89

(i) Construct a grouped frequency distribution table with classes

84 – 86, 86 – 88

(ii) Which month or season do you think this data is about?

(iii) What is the range of this data?

Solution:
(i) The grouped frequency distribution table for the given data is as follows:

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(ii) From the data we observe that relative humidity is high. So data appears to be taken in the rainy season.

(iii) From the data, we observe that

Highest relative humidity = 99.2%

Lowest relative humidity = 84.9%

Range = (99.2 – 84.9)% = 14.3%

Q3. The heights of 50 students, measured to the nearest centimeters, have been found to be as follows :

161 150 154 165 168 161 154 162 150 151

162 164 171 165 158 154 156 172 160 170

153 159 161 170 162 165 166 168 165 164

154 152 153 156 158 162 160 161 173 166

161 159 162 167 168 159 158 153 154 159

(i) Represent the data given above by a grouped frequency distribution table, taking the class intervals as 160 – 165, 165 – 170, etc.

(ii) What can you conclude bout their heights from the table?

Solution:
(i) The grouped frequency distribution table for the given data is as follows:

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(ii) From the frequency distribution table drawn above, we conclude that more than 50% of the students are shorter than 165 cm.

Q4. A study was conducted to find out the concentration of sulphur dioxide in the air in parts per million (ppm) of a certain city. The data obtained for 30 days is as follows :

0.03 0.08 0.08 0.09 0.04 0.17

0.16 0.05 0.02 0.06 0.18 0.20

0.11 0.08 0.12 0.13 0.22 0.07

0.08 0.01 0.10 0.06 0.09 0.18

0.11 0.07 0.05 0.07 0.01 0.04

(i) Make a grouped frequency distribution table for this data with class intervals as 0.00 – 0.04, 0.04 – 0.08 and so on.

(ii) For how many days, was the concentration of sulphur dioxide more than 0.11 parts per million?

Solution:
(i) The grouped frequency distribution table for the given data is as follows:

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(ii) From the above frequency distribution we observe that the concentration of Sulphur dioxide was more than 0.11 ppm for 8 days.

Q5. Three coins were tossed 30 times simultaneously. Each time the number of heads occurring was noted down as follows:

0 1 2 2 1 2 3 1 3 0

1 3 1 1 2 2 0 1 2 1

3 0 0 1 1 2 3 2 2 0

Prepare a frequency distribution table for the data given above.

Solution:
(i) The grouped frequency distribution table for the given data is as follows:

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Conclusion

In conclusion, these are quick and effective revision notes for the chapter. With regular practice, students will be able to solve all types of Statistics problems confidently. 

Revising these notes will give students an edge during exam preparation, as they are designed to help you revise faster and more efficiently, especially when time is limited.

FAQs

Q1. What is Statistics?

Ans. Statistics is the branch of mathematics that deals with the collection organisation, presentation, analysis and interpretation of data.

Q2. What is meant by ungrouped data?

Ans. Ungrouped data is data that is collected and presented without arranging it into class intervals or groups.

Q3. What is a frequency distribution table?

Ans. A frequency distribution table shows how many times each observation or group of observations occurs in a data set.

Q4. What is the difference between mean and median?

Ans. Mean is the average of all observations, while median is the middle value of the arranged data.

Q5. What is mode and when is it useful?

Ans. Mode is the value that occurs most frequently in a data set. It is useful when we want to know the most common value.