Tips And Tricks And Shortcuts For Elementary Statistics

Tips and Shortcuts to Solve Elementary Statistics:

Type 1: Find the Mean,Median and Mode of the following set of data.

2,5,3,4,2,7,9,2,3

Solution:

As we know through the given formulas, Mean = \frac {\text{sum of all the elements}}{\text{number of elements}}

= \frac{2+5+3+4+2+7+9+2+3}{9}

= \frac{37}{9}

=4.111

In order to find Median we’ll arrange the numbers in ascending order first.

=2,2,2,3,3,4,5,7,9

Since,the middle term of the series (in which number of observations is odd) is the median.

Hence,3 is the median of the above series.

Now, Mode=The most frequent value in the set

In the above set we can see 2 is the most number of repeated value hence,the mode is 2.

Type 2: Consider the following set of data and find the variance and the standard deviation.

2,4,4,4,5,5,7,9

Solution:

Mean of these numbers= \frac{2+4+4+4+5+5+7+9}{8}

= \frac{40}{8}

=5

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

= (2-5)^{2}=-3^{2}=9

= (4-5)^{2}=-1^{2}=1

= (4-5)^{2}=-1^{2}=1

= (4-5)^{2}=-1^{2}=1

= (5-5)^{2}=0^{2}=0

= (5-5)^{2}=0^{2}=0

= (7-5)^{2}=2^{2}=4

= (9-5)^{2}=4^{2}=16

= Variance=\frac{9+1+1+1+0+0+4+16}{8}

= Variance=\frac{32}{8}

=> variance=4 and,Standard deviation= \sqrt{4} =2

You can also solve more questions on elementary statistics to improve your command on this topic.