Elementary Statistics Formulae

Elementary Statistics Formulae

Statistics is a branch of mathematics that deal with the collection, organization, presentation, analysis and interpretation of data.In simple words statistics deals with data.

There are four measures of dispersion.These can be written as:

  1. Range
  2. Mean deviation
  3. Variance
  4. Standard deviation

Formulas:

1) Mean= \bar{x} =\frac{\sum x_{i}}{N}

x_{i}=\text{terms given}

N=Total number of terms

2) Mode=M=The value which occurs most frequently

3)Mean Deviation,M.D.= \frac{\sum |x_{i}-M|}{N} (from average deviation)

4)Variance, \sigma ^{2} =\frac{\sum(x_{i}-\bar{x})^{2}}{N-1}

5)Standard deviation, \sigma =\sqrt{variance}

= \sqrt{\frac{\sum(x_{i}-\bar{x})^{2}}{N}}

Know More About Elementary Statistics Terms

Mean:Mean can  be defined as the sum of all the elements divided by number of all elements.

Mean=\frac {\text{sum of all the elements}}{\text{number of elements}}

Median:Median is defined as the middle value of a set of data. If a set consists of an odd number of values, then the middle value will be the median of the set.Else, if the set consists of an even number of sets, then the median will be the average of the two middle values.

Mode:The mode can be defined as the most frequent value in the given set of data.

Variance:Variance is used to calculate the standard deviation.It is always positive.

Standard deviation:It is the square root of the variance.

Examples of how to find Mean,Median,Variance and Standard deviation

Example 1: Consider the data set containing the values 20, 24, 25, 36, 25, 22, 23.Find the mean of the data.

Solution:We know that ,

Mean=\frac {\text{sum of all the elements}}{\text{number of elements}}

Mean= \frac{20+24+25+36+25+22+23}{7}

=25

Example 2:For the above given data calvulate the median.

Solution:Re-arranging the above data in ascending order we get 20, 22, 23, 24, 25, 25, 36.

The middle value will be the median.

So,the middle value is 24.Hence,the median is 24.

Example 3:Calculate the mode for the above data.

Solution:The mode can be defined as the most frequent value in the given set of data.In the data given the most frequent value is 25 which occurred more than any other value.Hence the mode is 25.

Example 4:Calculate the range for the above set of data.

Solution:Range=higher value-lower value

=36-20

=16

Example 5:Calculate the variance of the set of data given.

Solution: \sigma ^{2} =\frac{\sum(x_{i}-\bar{x})^{2}}{N-1}

Mean of the data=25

now,using \sum(x_{i}-\bar{x})^{2}

20-25=-5 and square of -5=25

24-25=-1 and square of -1=1

25-25=0 and square of 0=0

36-25=11 and square of 11=121

25-25=0 and square of 0=0

22-25=-3 and square of -3=9

23-25=-2 and square of -2=4

Adding the squared difference,

25+1+0+121+0+9+4=160

and number of elements=7

Hence,Variance=\frac{160}{6}=26.667 (approximately)