Mathematics Notes for Class 11 Statistics

Statistics

Welcome to the chapter on Statistics for Class 11. In this chapter, you will learn how to collect, organize, represent, and analyze data. You will also understand important concepts like mean, median, mode, and measures of dispersion. By the end of this chapter, you will be able to solve problems using statistical methods and interpret real-life data.

Key Concepts

Statistics: The study of collecting, organizing, analyzing, and interpreting data.
Data: Information collected for analysis.
Frequency Distribution: A table that shows how often each value occurs.
Mean: The average of a set of numbers.
Median: The middle value in an ordered set of data.
Mode: The value that appears most often in a data set.
Measures of Dispersion: Ways to describe the spread of data (range, variance, standard deviation).

Types of Data

Primary Data: Data collected by the investigator for the first time.
Secondary Data: Data collected by someone else and used by the investigator.

Presentation of Data

Data can be presented using tables, bar graphs, histograms, and frequency polygons.
Organizing data helps in better understanding and analysis.

Measures of Central Tendency

Mean (Arithmetic Mean):
Mean = (Sum of all values) / (Number of values)
Median:
Arrange the data in order and find the middle value.
Mode:
The value that occurs most frequently in the data set.

Example: For the data 2, 4, 4, 6, 8:
Mean = (2+4+4+6+8)/5 = 24/5 = 4.8
Median = 4
Mode = 4

Measures of Dispersion

Range: Difference between the highest and lowest values.
Variance: The average of the squared differences from the mean.
Standard Deviation: The square root of the variance. It shows how much the data varies from the mean.

Example: For the data 2, 4, 4, 6, 8:
Range = 8 - 2 = 6

Cumulative Frequency and Ogive

Cumulative frequency is the running total of frequencies up to a certain point.
Ogive is a graph that shows cumulative frequency.

Practice Questions

Find the mean, median, and mode of the data: 5, 7, 7, 9, 10.
Calculate the range and standard deviation for the data: 3, 6, 9, 12.
Draw a bar graph for the following data: Apples - 10, Bananas - 15, Oranges - 8.
What is the difference between primary and secondary data?
Explain the use of cumulative frequency in statistics.

Challenge Yourself

Given the data: 2, 4, 6, 8, 10, calculate the variance and standard deviation.
Collect data from your classmates about their favorite sport and present it using a bar graph.

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

Mean: The average of a set of numbers.
Median: The middle value in an ordered data set.
Mode: The value that appears most often.
Range: The difference between the highest and lowest values.
Variance: The average of the squared differences from the mean.
Standard Deviation: A measure of how spread out numbers are from the mean.
Cumulative Frequency: The sum of frequencies up to a certain value.

Answers to Practice Questions

Mean = (5+7+7+9+10)/5 = 38/5 = 7.6; Median = 7; Mode = 7
Range = 12 - 3 = 9; Standard deviation = 3.87 (rounded to two decimals)
Draw bars for Apples (10), Bananas (15), Oranges (8) on graph paper.
Primary data is collected by the investigator; secondary data is collected by someone else.
Cumulative frequency helps in finding medians and drawing ogives.

Practice statistics to understand data and make smart decisions in real life!

Mathematics Class 11 - Statistics Notes