Class 9 Notes - Statistics

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1. Introduction to Statistics

Statistics is the branch of mathematics that deals with the collection, organization, analysis, interpretation, and presentation of data. It helps us make sense of information and draw conclusions from it.

2. Collection of Data

Data is a collection of facts, such as numbers, words, measurements, or observations. In statistics, we collect data to answer questions or solve problems.

  • Primary Data: Data collected by the investigator for a specific purpose (e.g., survey in your class).
  • Secondary Data: Data collected by someone else and used by the investigator (e.g., census data).

3. Organization of Data

Once data is collected, it needs to be organized for easy understanding. This can be done using tables, tallies, or charts.

  • Raw Data: Data as collected, not yet organized.
  • Frequency Distribution: Arranging data to show how often each value occurs.

4. Presentation of Data

Data can be presented visually to make it easier to interpret.

  • Bar Graph: Uses bars to show the frequency of different categories.
  • Histogram: Similar to a bar graph but used for continuous data, with no gaps between bars.
  • Frequency Polygon: A line graph that shows the frequencies of different values.

5. Measures of Central Tendency

These are values that represent a typical or central value for a set of data.

  • Mean (Average): Sum of all values divided by the number of values.
  • Median: The middle value when data is arranged in order.
  • Mode: The value that occurs most frequently in the data set.

6. Example

Given Data: 5, 7, 8, 7, 10, 7, 6

  • Mean: (5 + 7 + 8 + 7 + 10 + 7 + 6) / 7 = 50 / 7 ≈ 7.14
  • Median: Arrange data: 5, 6, 7, 7, 7, 8, 10. Middle value is 7.
  • Mode: 7 (appears most often)

7. Word Problems

  1. The marks obtained by 10 students in a test are: 8, 7, 9, 6, 7, 8, 7, 5, 6, 7.
    Find the mean, median, and mode.
  2. Draw a bar graph to represent the number of books read by students in a month: 2, 4, 3, 5, 4, 3, 2, 4.

8. Common Mistakes

  • Confusing mean, median, and mode.
  • Not arranging data in order before finding the median.
  • Forgetting to count all values when calculating the mean.

9. Practice Exercises

  1. Find the mean, median, and mode of: 12, 15, 12, 18, 20, 12, 15.
  2. Organize the following data into a frequency table: 3, 5, 3, 4, 5, 3, 4, 5, 4, 3.
  3. Draw a bar graph for the number of students in different classes: Class 6 - 30, Class 7 - 28, Class 8 - 32.

10. Summary

  • Statistics helps us collect, organize, and interpret data.
  • Data can be presented using tables and graphs.
  • Mean, median, and mode are measures of central tendency.
  • Visual representation makes data easier to understand.