Mathematics Class 10 - Statistics Notes

Statistics

Welcome to the chapter on Statistics for Class 10. In this chapter, you will learn how to collect, organize, represent, and analyze data. You will also learn about mean, median, mode, and how to solve problems using these concepts. By the end of this chapter, you will be able to interpret data and use statistical tools in real-life situations.

Key Concepts

• Data: Information collected in the form of numbers or facts.
• Frequency: The number of times a value appears in the data.
• Grouped Data: Data arranged in groups or classes.
• Ungrouped Data: Raw data not organized into groups.

Presentation of Data

• Data can be shown using tables, bar graphs, histograms, and frequency polygons.
• Tables help organize data for easy understanding.
• Bar graphs and histograms are used to visually represent data.

Measures of Central Tendency

Central tendency means finding a single value that represents the whole data set. The three main measures are:

• 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 appears most often in the data.

Formulas

• Mean (Ungrouped Data): Mean = (Sum of all values) / (Number of values)
• Mean (Grouped Data): Mean = (Σf_ix_i) / (Σf_i)
• Median (Grouped Data): Median = l + [(n/2 – F) / f] × h
• Mode (Grouped Data): Mode = l + [(f₁ – f₀) / (2f₁ – f₀ – f₂)] × h

Where:
l = lower class boundary of the median/modal class
n = total frequency
F = cumulative frequency before the median class
f = frequency of the median/modal class
h = class interval
f₀ = frequency of class before modal class
f₁ = frequency of modal class
f₂ = frequency of class after modal class

Practice Questions

1. Find the mean of the following data: 5, 8, 10, 12, 15.
2. The marks obtained by 7 students are: 12, 15, 11, 15, 14, 13, 15. Find the mode.
3. Arrange the data: 7, 3, 9, 5, 11. Find the median.
4. Draw a bar graph for the following data: Apples – 10, Bananas – 15, Oranges – 7.
5. Explain the difference between grouped and ungrouped data.

Challenge Yourself

• Given the following frequency distribution, find the mean:
  

  Class Interval	Frequency
  0-10	5
  10-20	8
  20-30	12
  30-40	10

• If the modal class of a grouped data is 20-30, l = 20, f₁ = 12, f₀ = 8, f₂ = 10, h = 10, find the mode.

Did You Know?

• Statistics is used in sports, weather forecasting, business, and many other fields.
• The word "statistics" comes from the Latin word "status," meaning state or condition.

Glossary

• Data: Information collected for reference or analysis.
• Frequency: Number of times a value occurs.
• Mean: The average of a set of numbers.
• Median: The middle value in an ordered data set.
• Mode: The value that appears most often.

Answers to Practice Questions

1. Mean = (5+8+10+12+15)/5 = 50/5 = 10
2. Mode = 15 (appears most often)
3. Arranged data: 3, 5, 7, 9, 11. Median = 7
4. Draw a bar graph with three bars for Apples (10), Bananas (15), Oranges (7).
5. Grouped data is organized into classes; ungrouped data is raw and not grouped.

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Practice statistics to understand and analyze data in everyday life!