Class 11 Statistical Tools and Interpretation

Statistical tools and interpretation are among the most important yet easiest units in Class 11th Economics. The unit is all about using different kinds of tools in order to analyse and interpret the data to extract something meaningful from it. The whole unit is numerically based and requires you to be good with numbers. It goes without saying how high‑scoring this unit can be if prepared properly. So, here we are with the summarised notes for class 11 Statistical Tools and Interpretation.

Topics Covered in Class 11th Statistical Tools and Interpretation

Here are the main topics covered in Class 11th Statistical Tools and Interpretation. You can take a look here:

Topics	Sub-topics
Measures of Central Tendency	Mean, Median, Mode
Correlation	Karl’s Pearson method, meaning etc.
Measures of Dispersion	Standard deviation, range, quartile deviation etc.
Introduction to Index Numbers	Use of index numbers.

Measures of Central Tendency

In class 11 Statistical Tools and Interpretation we will first begin with measures of central tendency. Measures of central tendency help in understanding data in a summarized way by identifying a central point of data. It basically means finding that central location, around which the data is clustered. Most commonly used measures of central tendency are mean, median, and mode. 

Let us understand each of these methods in a bit more detail:

Mean – The mean is a measure of the central tendency of the data and is also called the average of the numbers. The mean is found by adding all the numbers and dividing it by the number of values in the data set.

x1+x2+x3+……..+xn / n

For e.g., the strength of IIM Ahmedabad is 300, the strength of IIM Bangalore is 400, the strength of IIM Calcutta is 200 and the strength of IIM Shillong is 100, you need to find the mean of the strength of all four IIMs. 

You will start by adding all the numbers in the given data- 
300+400+200+100= 1000
Post that you need to divide this number by the number of values i.e. 250
Hence, 1000/4= 250

The mean of all four IIMs combined is 250.

This is the most basic concept behind finding mean but is most important as well. If you understand what is being done, no matter how tricky the question might be, you just need to remember the core concept.

Median – The median is defined as the middle value of the set. In order to find the median of a data set, you need to first arrange that set in ascending order and then:

• If the number of values is odd, pick the middle value , and that is your median.
• If the number of values is even, find the average of the middle two numbers and your median will be the answer you get.

Mode – The mode is the easiest measure of central tendency to calculate. It is the number that occurs the most number of times in a data set.

For eg: 2,3,4,2,5,2,2,2,5,9

The mode in the above data set will be 2 as it is the only number which has appeared 5 times in the above data set.

Measures of Dispersion – Statistical Tools And Interpretation

We now move on to Measures of Dispersion in class 11 Statistical Tools and Interpretation. When the values in a data set are large, the data set usually tends to scatter. Dispersion is basically used to measure the variation of an item and to measure how spread out a data set is.

Here are the methods for measuring dispersion- 

• Range
• Quartile Deviation
• Standard Deviation
• Mean Deviation

Range – The range of a data set is calculated by finding out the difference between the highest value and the lowest value of the data set. 

Quartile Deviation – Interquartile Range= Q3-Q1 (here, Q represents the quartile in the series)

Quartile deviation is defined as the semi‑interquartile range, i.e., (Q3− Q1) / 2

Standard Deviation – A standard deviation is a statistical tool which measures the dispersion in a data set with respect to its mean and is calculated as the square root of the mean of the squared deviations from the mean. 

How to Calculate Standard Deviation?

Direct Method – Standard deviation is calculated by dividing the sum total of the squares of deviation by the number of items and then finding its square root.

σ = √ΣX2 / N

Shortcut Method – This method assumes a suitable arbitrary value for deviations. 

σ = √[(∑D²/N) – (∑D/N)²]

Step-deviation Method – This method selects a common factor so that, when deviations are divided by it, the calculations simplify

σ= √[(∑D’²/N) – (∑D’/N)²]  × C

Also Read: Nature and Scope of Economics

Correlation – Statistical Tools And Interpretation

The next topic in class 11 statistical tools and interpretation is Correlation. Correlation is defined as a statistical tool which helps in understanding the relationship between two variables. It means how a change in one variable affects the other variable.

There are two types of correlation-

• Negative correlation- e.g., the relationship between price and demand of a product
• Positive correlation- e.g., the relationship between price and supply of a product

Methods to Calculate Correlation

• Scatter diagram – A scatter diagram is a type of method which helps in understanding the degree and direction of correlation. After plotting the variables, the clusters of points form a scatter diagram; their direction and closeness indicate the relationship between the two variables.
• Karl Pearson method – The Karl Pearson method is a completely quantitative method and provides numerical value in order to establish the intensity of the linear relationship between the two variables.
• Spearman’s rank correlation – This is a formula developed by Charles Edwards Spearman. It was devised to calculate the coefficient of qualitative variables. It is also known as Spearman’s Rank.

Introduction to Index Numbers

The last topic in class 11 statistical tools and interpretation is the introduction to index numbers. Index numbers are a statistical tool which helps in measuring variations between the related variables of a group. They act as a relative measure of a group of data and they offer a precise measurement of the quantitative change in the concerned variables.

Index numbers help in understanding the changes in the standard of living and act as a barometer for measuring changes in the purchasing power of money as well. Index numbers are also really helpful in major decisions related to businesses such as determining the rate of the premium.

 Also Read: What is the Difference Between Mathematics and Statistics?

Practice Questions for Class 11 Statistical Tools And Interpretation

Here are a few practice questions which will help you prepare this unit much better. 

• The coefficients of variations for the two distributions are 60 and 70 and their standard deviations are 21 and 16 respectively. Determine its arithmetic mean.
• The mean of 2, 7, 4, 6, 8 and p is 7. Find the mean deviation of the median of these observations.
•  If for the distribution (x-5)= 3, (x-5)2 = 43, and the total number of items is 18, determine the mean and standard deviation.
•  Find the mean deviation about the median for the following data: 36, 72, 46, 40, 60, 45, 5, 46, 51, 49
• The mean and the standard deviation of the 100 observations are found to be 40 and 10 respectively. If at the time of calculation, two observations were taken wrongly as 30 and 70 in place of 3 and 27 respectively. Determine the accurate standard deviation.

FAQs

Additional Reads
Economics Project for Class 12	Everything You Need to Know About Class 11 Economics
Commerce Subject in Class 11: With and Without Mathematics	Class 11 Maths Syllabus 2024-25: Revised Syllabus
Tongue Twisters in English for Students: 200+ Examples	Branches of Sociology

This was all about class 11 statistical tools and interpretation. We hope this blog was able to help you with your preparation. To read more informative articles like this one, keep following Leverage Edu!