# Chapter 6 – Statistics

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

Statistics is the branch of mathematics that deals with data collection and statistical representation of a particular analysed data. This mathematics branch deals with all the study, analysis, collection, representation, interpretation, organisation and presentation of the data in histograms, pie charts, bar graphs and other formats.

#### Different Types of Data

Before we start with the data type, we need to understand what exactly data means. We can define Data as the collection of facts and figures that can help you conclude. Apart from the facts, data can be the collection of words, numbers, observation and measurements. Here are the types of data:

• Qualitative Data: The first category of data is the qualitative data related to the description of a person, thing or entity.
• Quantitative Data: The second is quantitative data that is numerical information about a thing or entity.
• Discrete data: This is the category of data with a particular fixed value and can be counted.

Continuous Data: All the data with a range and no fixed value is categorised under continuous data. One can measure the data.

#### Types of Data Representation

When it comes to data representation, we already know many different ways like Pie charts, Bar charts, etc. Every data can be represented differently. Here are some of the common ones.

• Histogram

A histogram is something similar to the bar graph but a complex version of it. In a histogram, you have the X and Y axis that has rectangles in the entire diagram. Each rectangle’s length or proportion shows the frequency of a particular variable whose class interval is depicted by the rectangles’ width. There should be no gaps between bars as it represents the continuous group data.

• Frequency distribution

Amongst all the representations, the first one that we learn at a young age is the frequency distribution. It is a collection of data values of a variable which is commonly represented as “f”. The table is made using the set of data and arranging them in ascending order of their frequency or magnitude.

• Ogive

Ogive, also known as a cumulative frequency curve, is also an essential part of this chapter. It is the representation of the cumulative frequency distribution of any given grouped data. It is also termed as one of the most efficient ways to analyse data to derive results.

#### Mean

One of the essential elements of the statistics chapter is mean. The arithmetic mean of any data is found using the method:

Mean= Sum of all observation/ Total number of observation

Or Mean x¯ = ∑x/n

X bar is the arithmetic mean in the formula, and the sum of all the observations divided by the total number of observations gives the mean.

#### Median

The Median of the set of data is defined as the mid-value or middlemost observation of given data. The condition that it needs to satisfy is that the data should be arranged in ascending order. When finding the median, there are two formulas that we use.

When the total number of observations is odd. The formula that is used when n is odd:

Median = [(n+1)/2]th observation

When the total number observations is even the formula that has to be used is:

Median = [(n/2) + (n/2+1)] / 2

Therefore, when you are asked to find the median of a set of observations, you should count the total number of observations first.

This formula is used to get the midpoint of all the observations when the number of observations is more. In this, n is the variable that depicts the total number of observations given in the question. Just insert the value and get the answer.

There is another way by which one can find the median. This formula has to be used when you get a table consisting of grouped data.

Median= l+[ (n/2-c)/f ]xh

or

Median= Mean/{(n/2+1)th +(n/2)th}observations

#### Mode

The third and another essential calculation that is asked to do in statistics is to find the mode. It is defined as the value that has the most frequency in a table. For ungrouped data, it is easy to find the mode as you need to check the value given the most number of times. But when it comes to Grouped data, things do change.

In ungrouped data, the formula to determine mode will be,

Mode= l + [ (fm – f1) / ( 2fm- f1 – f2) ] x h

#### Conclusion

In this chapter, students learn about the basics of statistics, formulas for mean, median, mode. We learned the types of data representation which includes the use of histograms, frequency distribution and ogive. We also saw the different types of data we study in statistics.

#### FAQs

1. What is statistics?
Statistics is the branch of mathematics that deals with data collection and statistical representation of a particular analysed data.
2. What are all types of data representations called statistics?
When represented as a pie chart, bar graph, histogram, line graph, pictographically, or frequency distribution, a data collection is called statistics.
3. What examples can you give of collecting data from day-to-day life?
Increase in our country’s population in the last two decades, the number of tables and chairs in a classroom.

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### High School Physics

• Alternating Current
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### High School Chemistry

• Acids, Bases and Salts
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• Absorption and Movement of Water in Plants
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• Principles of Inheritance and Variation
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• The Endocrine System
• The Fundamental Unit Of Life
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• The Nervous System and Sense Organs
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• Transport in Plants

### High School Math

• Algebra – Arithmatic Progressions
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### Middle School Science

• Acids, Bases And Salts
• Air and Its Constituents
• Basic Biology
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• Universe
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• Water: A Precious Resource
• Weather, Climate And Adaptations Of Animals To Climate
• Winds, Storms And Cyclones

### Middle School Math

• Addition
• Area and Its Boundary
• Boxes and Sketches
• Data Handling
• Fun With Numbers
• Heavy and Light
• How Many
• Long And Short
• Mapping
• Measurement
• Money
• Multiplication and Factors
• Multiply and Divide
• Numbers
• Parts and Wholes
• Pattern Recognition
• Patterns
• Play With Patterns
• Rupees And Paise
• Shapes And Angles
• Shapes And Designs
• Shapes and Space
• Similarity
• Smart Charts
• Squares
• Subtraction
• Tables And Shares
• Tenths and Hundredths
• Time
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