Statistics Revision Notes

Revision is a very important part of every student's life. Especially, during the board exams. Statistics is a branch of mathematics, which deals with the study of organizing, gathering, calculating, interpreting, and showing the data. Statistics is chapter 14 in the NCERT textbook. This chapter mainly discusses statistical concepts and their related topics. The following are the subtopics of this chapter, ungrouped data, grouped data, and the count of central tendencies such as mode, mean, median, and to find the respective mean, median, and mode, with examples of each. 

Statistics are very helpful in our day to day too, when it is represented with a particular number which represents all the numbers, this is called the measure of central tendency, mainly they are called the mean, median, and mode. Statistics is a mathematical science including methods of collecting, organizing and analysing data in such a way that meaningful conclusions can be drawn from them. In general, its investigations and analyses fall into two broad categories called descriptive and inferential statistics.

Descriptive statistics deals with the processing of data without attempting to draw any inferences from it. The data are presented in the form of tables and graphs. Simple terms are used for describing the characteristics of the data. Events that are dealt with include everyday happenings such as accidents, prices of goods, business, incomes, sports and population data.
Inferential statistics is a scientific discipline that uses mathematical tools to make forecasts and projections by analysing the given data. This is of use to people employed in such fields as engineering, economics, biology, the social sciences, business, agriculture and communication

Mean:

It is defined as the sum of all the values divided by the total number of values, where x1, x2, x3 are values and xn is the last value and n is the total number of values. 

 Mean = x1,x2,x3...xn/n 

This can also be found when the class intervals are not given.

Mean=xi fi, where fi is the frequency of ith observation/ value x1.

This also can be done when there are class intervals present.

Mean =xi fi, where fi is the frequency of ith class whose class mark is x1.

Median:

Given there are sets of values; it must be either in an ascending or a descending order. The centre value or the middle value is told to be the median. 

If the number of the values is even then the n/2th and n+1/2th observations are said to be the median.

Whereas, if there is an odd number of values, the n+12th observation is said to be the median. 

Mode:

It is the number, which occurs the most times in a series or a set of values.

Frequency:

Frequency is the number of times a particular value repeats or occurs in a set of values or data.

Class Interval:

Various data can be collectively grouped into separate classes such that all the values of observations in a particular range will belong to that particular class.

Class Width:

It is the upper class subtracted by the lower class.

Class mark:

Class mark is said to be the upper-class limit deducted by the lower-class limit; the whole divided by two.

Ungrouped Data:

This type of data is the one in which the values are unaltered and untouched by rearranging. For example; the amount of prices of different fruits per kg; Rs.12, Rs. 23, Rs. 11, Rs. 31, etc. Ungrouped data set is mostly easy to work with when the values are smaller in number. This data shows that some fruits are more expensive than others. 

Grouped Data:

This type of data is more organized and well placed in order to make it easier to handle the values.

For example: the height and age of various students;

This shows that many students have different heights with respect to their age group. This makes it very much easier to calculate the values and make it nice and organized. 

Directing Method of Finding Mean:

First, we need to arrange the data into intervals and then we must search for the respective frequency of every class. Next, we must take the midpoint of the lower class and upper-class limits. Then, we need to make a tabular column of the product and its respective frequency for the class. Later, we must calculator their sum (xifi) and divide the found sum by the sum of the frequencies (fi) to get the final answer that will be the Mean.

The Relation between Mean of Deviations and Mean:

In a given data set, the statistical count or measure, which is mostly used to calculate accurately the average deviation from the mean value, is called Mean Deviation. There are various methods that are used to calculate the mean deviation; here is a step-by-step procedure on how to calculate it:

• First, we need to take the given data set and its values and we find the mean value.
• Next, deduct the data value from the mean value while ignoring the plus or minus symbols.
• Now, find the mean of those values, which we have received, in the previous step.

Mean Deviation Formula:

Mean = [χ-μ] ? N

X is the value of each and every data set;
M is the mean value of the present data set,

And N is the total number of data values.

Cumulative Frequency:

It is received by adding all the frequencies up to a certain point.

Cumulative Frequency distribution of less-than type:

The less than type indicates the number of observations that are less than or equal to a particular observation.

Cumulative Frequency distribution of more-than type:

The more than type indicates the number of observations that is greater than or equal to a particular observation.