Statistical tools and interpretation are one of the most important yet easiest units in **class 11th Economics.** The unit is all about using different kinds of tools in order to analyze 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 scoring this unit can be if prepared properly. So, here we are with the summarized notes for class 11 Statistical Tools and Interpretation.

Here are the main topics covered in Class 11 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 that by a number of values in the data set.

**x1+x2+x3+……..+xn / n**

For eg: 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 no of values is odd – you just pick the middle value and that is your median.
- If the no. of values is even – find the average of the middle two numbers and your median will be the answer you get.

**Mode** – 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.

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 see how to spread out a data set.

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 (symbol Q represent 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 squares of items from the mean values.

### 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

**Short-cut method –** This method assumes any random value for deviation.

σ = √[(∑D²/N) – (∑D/N)²]

**Step deviation Method –** This method selects a* *common factor among deviations so that when deviations get divided by this factor, deviation gets reduced, thus making the calculation simpler.

σ= √[(∑D’²/N) – (∑D’/N)²] × C

Also Read: **Application of Statistics**

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- eg: price and demand of a product
- Positive correlation- eg: 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 all the variables are plotted on the graph, those clusters of points are called a scatter diagram and their overall direction and their degree of closeness tell us about the relationship of 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**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 money as well. Index numbers are also really helpful in major decisions related to businesses such as determining the rate of the premium.

Explore:** What is the Difference Between Mathematics and Statistics?**

Here are a few practice questions which will help you prepare the chapter class 11 statistical tools and interpretation 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.

## Important Questions and Answers

**Q1. What is the difference between median and mode?**

Ans: The median is a value in a series that is in the middle, with half of the values above it and the other half below it, whereas the mode is a value that appears regularly in the series. The modal value has the highest frequency in the sequence, indicating that it is the most common.

**Q2. What is the partition value?**

Ans: partition value is the value that divides the series into more than two parts known as a partition value.

**Q3. What do you understand by central tendency?**

Ans: The term “central tendency” refers to all statistical analysis approaches that examine the average of statistical series.

**Q4. What is meant by dispersion and coefficient of dispersion?**

Ans: The coefficient of dispersion indicates different data percentages or relative values, while dispersion is a calculation of how much different objects appear to dispense away from the central tendency. A relative indicator of dispersion is the coefficient of dispersion.

**Q5. Briefly explain the interquartile range.**

Ans: The interquartile range is the difference between the first and third quartiles (Q1 and Q3) in a sequence.

**Q6. What do you understand by mean deviation and standard deviation?**

Ans: Mean deviation is a mathematical average of all the principles’ deviations taken from some average value (mean, median, mode) of the sequence, ignoring the signs (+ or -) of the deviation. On the other hand, The square root of the geometric mean of the products’ squared deviations from their mean value is the standard deviation.

**Q7. Define correlation and partial correlation.**

Ans: A statistical method or technique that measures a quantitative relationship between different variables, such as demand and price, is called correlation. When there are more than two variables, and the relationship between only two of them is suitable for treating the other variables as constant, then it is said that the correlation is partial.

**Q8. What do you mean by the line of best fit?**

Ans: The best-fit line is one that passes through all of the scattered points and represents the majority of them. Half of the scattered points should be on each side, roughly.

**Q9. Explain the difference between negative and positive correlation?**

Ans: The difference between negative and positive correlation is that positive correlation involves variables moving in the same direction, whereas negative correlation involves variables moving in the opposite direction.

**Q10. Correlation coefficients range from -1 to +1. In arithmetic terms, how would you put it?**

Ans: Correlation is perfect negative when the coefficient of correlation is -1, and perfect positive when the coefficient of correlation is +1.

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**!