Solve Elementary Statistics Problems

Introduction of elementary statistics problem:

Data is a word in a plural form of the Latin word datum. Every part of our lives utilizes data in one form or the other. This extraction of significant information is study in a branch of mathematics called statistics. A step additionally by studying certain numerical representatives of the ungrouped data, also called measures of central tendency, namely, mean, median, mode and also range are under the elementary statistics only.

I like to share this How to Find the Mean Median and Mode with you all through my article.

About Elementary statistics


Elementary statistics is deals with the basic static calculations of data’s for finding the mean values etc... The word ‘statistics’ appears to have been taken from the Latin word ‘status’ meaning ‘a state (related to a political)’... Statistics deals with collection, organization, analysis, and Interpretation of data. ‘Statistics’ has held different meanings in different contexts, so that the calculation process is based on the meaning and data. Elementary statistics problems are mainly deals with the mean, median, mode, and range.

Example for elementary statistics problems


Let us see about the basic elementary stastistics problem below,
Example for Mean: what is the mean of 3, 8 and 5?
Add the numbers: 6 + 8 + 4 = 16
divide by how many numbers (i.e. we added 3 numbers): 18 ÷ 3 = 6
so the Mean is 6
Example for Median: Find the Median of {12, 3 and 5}. Put them in order: {3, 5, 12}, the middle number is 5, so the median is 5.
Special Case: If there are two middle numbers (as happens when there are an even amount of numbers) then average those two numbers.
Find the Median of {12, 3, 5 and 2}. Put them in order: {2, 3, 5, 12}, the middle numbers are 3 and 5, the average of 3 and 5 is 4, so the median is 4.
Example for Mode: The number, which appears mostly, repeated in a set of numbers. In Set {6, 3, 9, 6, 6, 5, 9, 3} the Mode is 6.
Example for Range: is nothing but the difference between the lower and higher values.
In {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9, so the range is 9-3 equals 6.
Range can also mean all the output values of a function.

Elementary Statistics Homework

Introduction to elementary statistics homework:

Our world is flattering more and more information oriented. Every part of our lives utilizes data in one form or the other. So, it becomes necessary for us to know how to extract meaningful information from such data. This taking out of meaningful information had studied in a branch of mathematics called Statistics.


elementary statistics homework Problems of find median:


Statistics example:

The points scored by a Tennis team in a series of matches are as

Follows:

20, 5, 10, 30, 18, 8, 17, 11, 14, 27, 51, 13, 11, 10, 21, 31

Find the median of the points scored by the team.

Statistics solution:

To arrange the given points in ascending order, we get

5, 8, 10, 10, 11, 11, 13, 14, 17, 18, 20, 21, 27, 30, 31, 51

There are 16 terms. Therefore, there are two middle terms.

That is, (16/2)th term and ((16/2)+1)th term. Therefore, these are the 8th and 9th terms.

Hence, the median is the average values of the 8th and 9th terms.

Median (14+17)/2=15.5

Therefore, the medial point scored by the Tennis team is 15.5.

I have recently faced lot of problem while learning What Does Mean Median and Mode Mean, But thank to online resources of math which helped me to learn myself easily on net.

elementary statistics homework Problems of find mode:


Statistics example 1:

Find the mode of the following numbers (out of 10) obtained by 20 peoples:

4, 6, 5, 8, 3, 2, 7, 7, 6, 5, 4, 8, 10, 10, 3, 4, 7, 6, 8, 8

Statistics solution:

We arrange this data in the following form:

2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 10, 10

Here 8 occur most frequently, i.e., four times. Therefore, the mode is 8.

Statistics example 2:

A team in a series of 10 matches given below scored the number of goals:

2, 5, 4, 3, 0, 1, 5, 5, 4, 5

Find the mode of these scores.

Statistics solution:

We arrange this data in the following form:

0, 1, 2, 3, 4, 4, 5, 5, 5, 5

Here 5 occur most frequently, i.e., four times. Therefore, the mode is 5.

These are some of the homework problem on elementary statistics.

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.