Measures of central tendency

Hello students, in this blog we are going to discuss the measures of central tendency that are the very important concept in the statistics. The most important central tendency measures are mean, median and mode. We calculate the mean, median and mode for the ungrouped data and we can calculate the mean, median and mode also for grouped data. Let’s discuss the all measure one by one.
Mean: - It means average of the whole numbers, like we have 9 numbers then we will add the 9 numbers together and divide by the 9, 9 is because total number are 9. For example: -
8, 7, 6, 8, 7, 5, 7, 6, 5, 6
Then add the all number and divide the total sum by 10, because 10 numbers are there.
8 + 7 + 6 + 8 + 7 + 5 + 7 + 6 + 5 + 6 / 10,
6.5 is mean,
This example was for the ungrouped data. We can calculate the mean when we have grouped data, to do this we have three methods they are: -
-Direct method.
-Shortcut method.
-Step-deviation method.
The all three methods have their respected formulas.
Medan (from CBSE Books): - Median is the middle value in the number distribution. Like we have 7 numbers then the median will be 4^th number and if we have 6 number then add the 3^rd and 4^th number and divide it by the 2, then he result will be median. For example 6, 7, 5, 4, 2 then the median is 5.
Mode: - The mode or mode value of a distribution is that value of the variable for which the frequency is maximum. For example 2, 6, 7, 2, 5, in this 2 is mode, because it is occurring at 2 times.


In upcoming posts we will discuss about Conditional probability and Conditional statements. Visit our website for information on Confidence Interval Formula

Types of events

Types of events in probability and statistics:
There are various types of events in probability and statistics:

1. Simple event: If the event consists of less than 2 elements from the sample space then it is called a simple event or elementary event.

If sample space is S = 2, 3, 4, 5, 6.
And if event is E = 3, then it is a simple or elementary event.

1. Compound event: It comes under the types of events in probability and statistics as if the event consists of more than one element or sample points from the sample space then it is called a compound event.

If sample space of throwing a dice is, S = 1, 2, 3, 4, 5, 6.
And if event is, E = 1, 3, 5, then it is known as a compound event.

1. Sure event or certain event: It comes under the types of events in probability and statistics (for more visit this)as if the sample space is, S = 1, 2, 3, 4, 5, 6 and the event is also same as that of sample space, i.e., E= 1, 2, 3, 4, 5, 6 which is also the subset of S and it occurs whenever an experiment is performed. Therefore, the event E is called as a sure event or certain event.

1. Mutually exclusive events: It comes under the types of events in probability and statistics as  if we consider a random experiment of throwing a dice and sample space is, S=1, 2, 3, 4, 5, 6. Two events associated with the above experiment are called mutually exclusive if both the events cannot occur at the same time or in the same trial. Like A=1, 3, 5 and B=2, 4, 6 are mutually exclusive events. If the events are A = 1, 2, 4 and B= 2, 5, 6 are not mutually exclusive as 2 is favorable to both the events.

1. Exhaustive Events: It comes under the types of events in probability and statistics for any random experiment, S, E1, E2, E3,….En are the events which are the subsets of S.

E1, E2, E3,…..En are consider as exhaustive events if the union of all of them is equal to S, i.e.,
E1 U E2 U E3 U ….U En = S
The above equation also proves true if the set of events E1, E2,…En are mutually exclusive and exhaustive events.

1. Null event: This event is always added in the sample space as a sample point called φ(fi).  This event is the subset of S and is called as null event or impossible event.

In upcoming posts we will discuss about Permutations and combinations and Intersection of a plane with 3-d figures. Visit our website for information on Measures of Central Tendency

Measures of central tendency in Grade XI

In this section we are going to discuss the topic Central tendency and how to calculate measures of central tendency. Central tendency for grade XI  of Andhra Pradesh board textbooks means calculation of the average data or number among the data set or large amount of data. Measuring central tendency is a process which has basically three types as Mean, Median and Mode. You can improve your math skills by playing measures of central tendency worksheets
First we discuss about the Mode that is the value that occurs many times in a data set. It can also have the frequency of the repeated numbers as an example a group of data set have the ten numbers as 92 , 100 , 103 , 98 , 100 , 95 , 100 , 99 ,100 ,92 then 100 is the number which occurs 4 times in the data set so 100 is the mode of this data set .
Another measure of central tendency is median that is defined as the value which is occurs in the middle of ordered data set. We also describe it by an example as 32 , 78 , 45 , 36 , 90 , 89 , 35 , 56 then when we arrange it in order as 32 , 35 , 36 ,44 , 56 , 78 , 89 , 90 then 45 and 56 is the middle values of ordered data set then the median of it is ( 44 + 56 ) / 2 = 100 / 2 = 50 .
There is another way of measuring central tendency (for more visit here) known as mean that is normally an arithmetic mean which is equal to the sum of the value s of data set which is divided by total number of values. It is often known as average. We can also understand it by an example as a data set of values as 4 , 6 , 8 , 3 , 5, 10have the mean value ( 4 + 6 + 8 + 3 + 5+ 10)/6= 36 / 6 =6 where total number of values are 6 and their total is 36 and when divide 36 by 6 then coming value is known as mean.

In upcoming posts we will discuss about Methods of data representation and Triangle congruence relationships. Visit our website for information on Z score Table