Elementary Statistics Problems

Introduction to elementary statistics problems: 

Elementary statistics problems were done normally with data collected for specific purposes. In elementary statistics problems, we make decisions about the data by analyzing and interpreting it. There are several methods in elementary statistics for representing data graphically and in tabular form.

The method used in elementary statistics for finding a representative value for the given data are called the measure of central tendency. The three measures of central tendency used in elementary statistics problems are  Arithmetic Mean, also median and mode.

Examples on Elementary Statistics Problems

Example 1:

Find the mean deviation of the mean for given data:

8,5,15,9,13,2,6,14

Solution:

Step 1 Mean of the given data are  `barx`


`barx`  = `(8+5+15+9+13+2+6+14)/8` = `72/8` = 9

Step 2 The deviations of the respective observations from the mean x, i.e., xi– x are
8– 9,5–9,15–9,9–9,13–9,2–9,6–9,14–9      ( or )   –1,–4,6,0,4,–7,–3,5

Step 3 The absolute values of the deviations, i.e.,|xi - x |are  -1,-4,6,0,4,-7,-3,5


Step 4 The required mean deviation about the mean is

M.D. (`barx` ) = `sum` 8 i-1 |xi-x| / 8

= `(1+4+6+0+4+7+3+5)/8 ` = `30/8` = 3.75

Example 2:

Find the mean deviation of the mean for given data :

13, 4, 19, 18, 5, 10, 18, 20, 21, 8, 15, 18, 2, 3, 16, 11, 3, 1, 10, 5

Solution:

find the mean ( `barx` ) of the given data

`barx` = `1/20` `sum` 20i-1  xi = `220/20` = 11


The respective absolute values of the deviations from mean, i.e.,|x-`barx` | are

2,7,8,7,6,1,7,9,10,3,4,7,9,8,5,0,8,10,1,6

Therefore
`sum` 20i-1 |xi - `barx` | = 118

and M.D. ( `barx` ) = `118/20` = 5.9

Examples on Elementary Statistics Problems

Example 3:

Find the mean deviation of the median for the following data: 5,11,7,5,14,12,20,6,8,21,23.

Solution :

Here the total number of observations is 11 which is odd. Arranging the data into ascending order,

5 , 5 , 6 , 7 , 8 , 11 , 12 , 14 , 20 , 21 , 23

Now Median =(11+1/2) or 6th observation = 11

The absolute values of the respective deviations from the median, i.e.,|xi - M| are

6 , 6 , 5 , 4 , 3 , 0 , 1 , 3 , 9 , 10 , 12
Therefore

? 11i-1 |xi - M| = 59

M.D.(M) = `1 / 11` ? 11i-1 |xi - M| = `(1 / 11) * 59`   = 5.36

Example 4:

Find the mean deviation of  the median for the following data: 10,5, 6, 3, 12, 11, 18, 4, 7, 18, 22.
Solution:

Here the total number of observations is 11 which is odd. Arranging the data into

ascending order, we have 3 , 4 , 5 , 6 , 10 , 11 , 12 , 18 , 18 , 19 , 22

Now Median =(11+1/2) or 6th observation = 11

The absolute values of the respective deviations from the median, i.e.,|xi - M| are

8 , 7 , 6 , 5 , 1, 0 , 1, 7 , 7 , 8 , 11
Therefore
`sum` 11i-1 | - M| = 61

and  M.D.(M) = 1/1111i-1 |xi - M| =` 1/11*61 ` =5. 545.