Statistics Class 9 NCERT: The Complete Guide

Collection of Data: The First Step in Statistics

Everything in statistics begins with data. But what is data? Data is simply a collection of facts, such as numbers, words, measurements, or observations. Think about the heights of all students in your class or the number of cars passing your house every hour – that's data! The purpose of collecting this data is to extract useful information from it.

There are two main types of data you will encounter:

1. Primary Data: This is data that you collect yourself for a specific purpose. It is first-hand information. For example, if you want to know the favourite sport of students in your class and you go to each student and ask them personally, the information you gather is primary data. It's original and collected directly by the investigator.

1. Secondary Data: This is data that has already been collected by someone else for their own purpose, but you are using it for your investigation. For example, using the population data from the Census of India website, looking up past weather records from the meteorological department, or getting cricket match scores from a sports website are all examples of using secondary data. This data is readily available and saves time, but we must ensure it comes from a reliable source.

How to Create a Grouped Frequency Distribution Table

1. Step 1: Determine the Range — First, look at your raw, unorganized data. Find the highest (maximum) and lowest (minimum) values. The range is the difference between the maximum and minimum values. Range = Maximum Value - Minimum Value. This helps you understand the spread of your data.
2. Step 2: Decide on Class Intervals — Decide how many groups (or classes) you want to divide your data into. The size of each group is the class size or class width. For Class 9, these intervals should be continuous (e.g., 0-10, 10-20, 20-30). Make sure the classes cover the entire range of your data.
3. Step 3: Use Tally Marks — Create a table with three columns: Class Interval, Tally Marks, and Frequency. Go through your raw data one value at a time. For each value, place a tally mark (|) next to the class interval it falls into. Remember, every fifth tally mark is a diagonal line across the first four (||||).
4. Step 4: Count the Frequencies — Once you have put a tally mark for every data point, count the tally marks for each class interval. Write this count in the 'Frequency' column. The total of all frequencies should equal the total number of data points you started with.

Worked Example: Creating a Histogram

• Problem: The marks obtained (out of 50) by 30 students of Class IX in a test are given below: 39, 25, 5, 33, 19, 21, 12, 41, 12, 21, 27, 17, 4, 33, 29, 17, 48, 9, 12, 38, 40, 29, 25, 27, 41, 17, 33, 40, 21, 25. Present this data in the form of a grouped frequency distribution table with class intervals 0-10, 10-20, etc., and then draw a histogram.
• Step 1: Create the Frequency Distribution Table. We first organize the data into a table. | Marks (Class Interval) | Tally Marks | Frequency | |------------------------|-------------|-----------| | 0-10 | ||| | 3 | | 10-20 | |||| || | 7 | | 20-30 | |||| |||| | 9 | | 30-40 | |||| | | 6 | | 40-50 | |||| | 5 | | Total | | 30 |
• Step 2: Draw the Axes and Choose a Scale. - Draw a horizontal axis (X-axis) and a vertical axis (Y-axis). - On the X-axis, represent the Marks (Class Intervals). Since the classes start from 0 and are continuous, we can mark 0, 10, 20, 30, 40, 50 at equal distances. - On the Y-axis, represent the Frequency. The highest frequency is 9, so we can choose a scale like 1 cm = 2 students.
• Step 3: Draw the Bars. - For each class interval, draw a rectangular bar with the width equal to the class size (10 units) and height corresponding to the frequency of that class. - For 0-10, the height is 3. - For 10-20, the height is 7. - For 20-30, the height is 9. - For 30-40, the height is 6. - For 40-50, the height is 5. - Important: Since the class intervals are continuous, there should be no gaps between the bars. The resulting graph is a histogram.

Exam Tips: Bar Graph vs. Histogram

A very common point of confusion for students is the difference between a bar graph and a histogram. Getting this wrong can cost you easy marks in an exam!

Use a Bar Graph when:

• The data is discrete or categorical. This means it represents separate items like 'favourite colours' (Red, Blue, Green), 'modes of transport' (Bus, Car, Cycle), or even shoe sizes (5, 6, 7).
• The bars have gaps between them to show that the categories are distinct.

Use a Histogram when:

• The data is continuous and has been grouped into class intervals (like 0-10, 10-20, 20-30 for marks, or 150-155, 155-160 for height in cm).
• The bars have no gaps between them, showing that the data flows from one interval to the next.

Pro Tip: Always label your axes clearly with what they represent (e.g., 'Marks' on the x-axis, 'Number of Students' on the y-axis) and state the scale you have used (e.g., On Y-axis: 1 cm = 5 students).

Practice Questions with Solutions

• Q: The blood groups of 30 students of Class IX are recorded as follows: A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O. Represent this data in the form of a frequency distribution table. Which is the most common, and which is the rarest, blood group among these students? A: Step 1: Create a table with three columns: Blood Group, Tally Marks, and Frequency. Step 2: Go through the list and make a tally mark for each blood group. A: |||| |||| (9) B: |||| | (6) O: |||| |||| || (12) AB: ||| (3) Step 3: Count the tally marks to find the frequency for each group. | Blood Group | Tally Marks | Frequency | |-------------|----------------|-----------| | A | |||| |||| | 9 | | B | |||| | | 6 | | O | |||| |||| || | 12 | | AB | ||| | 3 | | Total | | 30 | Step 4: Analyze the table to find the most common and rarest blood groups. The highest frequency is 12, which corresponds to blood group O. The lowest frequency is 3, which corresponds to blood group AB. Final answer: The most common blood group is O, and the rarest blood group is AB.
• Q: The following are the heights (in cm) of 20 students: 155, 152, 161, 158, 154, 159, 160, 153, 156, 162, 157, 151, 163, 158, 155, 160, 157, 152, 159, 158. Prepare a grouped frequency distribution table with a class size of 5, starting from 150-155. A: Step 1: Find the range of the data. Maximum value = 163, Minimum value = 151. Range = 163 - 151 = 12. Step 2: Create class intervals of size 5, starting from 150-155. The classes will be 150-155, 155-160, and 160-165. Note that 155 will be included in the 155-160 class, not 150-155 (upper limit is excluded). Step 3: Use tally marks to organize the data into these classes. 150-155: 152, 154, 153, 151, 152 (5 students) 155-160: 155, 158, 159, 156, 157, 158, 155, 157, 159, 158 (10 students) 160-165: 161, 160, 162, 163, 160 (5 students) Step 4: Create the final frequency table. | Height (cm) | Tally Marks | Frequency | |-------------|--------------|-----------| | 150-155 | |||| | 5 | | 155-160 | |||| |||| | 10 | | 160-165 | |||| | 5 | | Total | | 20 | Final answer: The grouped frequency distribution table is as shown above.
• Q: Why is there no gap between the bars of a histogram? A: Step 1: Recall the type of data a histogram represents. A histogram is used to represent continuous data that has been grouped into class intervals. Step 2: Understand the meaning of continuous class intervals. Intervals like 10-20, 20-30, 30-40 mean that the data flows without any break. The point where one interval ends (e.g., 20) is the same point where the next interval begins. Step 3: Connect the continuous nature of data to the graphical representation. To visually represent this continuity and the absence of gaps in the data ranges, the bars of the histogram are drawn adjacent to each other, with no space in between. Final answer: There are no gaps between the bars of a histogram because it represents continuous data grouped in class intervals. The bars touch each other to show that there are no gaps in the data values from one interval to the next.
• Q: What is the main difference between primary and secondary data? A: Step 1: Define primary data. Primary data is original, first-hand information collected by the investigator or researcher for a specific purpose. Step 2: Define secondary data. Secondary data is second-hand information that was already collected by someone else for another purpose, but is now being used by the investigator. Step 3: State the core difference based on the definitions. The main difference lies in the source and originality. Primary data is collected directly from the source, while secondary data is obtained from existing sources like government reports, websites, or published articles. Final answer: The main difference is that primary data is collected first-hand by the investigator for their specific study, whereas secondary data is data that has been pre-collected by someone else.

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