# COMPARING DIFFERENCES IN CENTERS TO VARIABILITY

## About "Comparing differences in centers to variability"

Comparing differences in centers to variability :

Recall that to find the mean absolute deviation (MAD) of a data set, first find the mean of the data. Next, take the absolute value of the difference between the mean and each data point. Finally, find the mean of those absolute values.

## Comparing differences in centers to variability - Example

The tables show the number of minutes per day students in a class spend exercising and playing video games. What is the difference of the means as a multiple of the mean absolute deviations ?

Solution :

Step 1 :

Calculate the mean number of minutes per day exercising.

0 + 7 + 7 + 18 + 20 + 38 + 33 + 24 + 22 + 18 + 11 + 6  =  204

Divide the sum by the number of students.

204 ÷ 12  =  17

Step 2 :

Calculate the mean absolute deviation for the number of minutes exercising.

 |0-17|  =  17|7-17|  =  10|7-17|  =  10|18-17|  =  1|20-17|  =  3|38-17|  =  21 |33-17|  =  16|24-17|  =  7|22-17|  =  5|18-17|  =  1|11-17|  =  6|6-17|  =  11

Find the mean of the absolute values.

17 + 10 + 10 + 1 + 3 + 21+ 16 + 7 + 5 + 1 + 6 + 11  =  108

Divide the sum by the number of students.

108 ÷ 12  =  9

Step 3 :

Calculate the mean number of minutes per day playing video games. Round to the nearest tenth.

13+18+19+30+32+46+50+34+36+30+23+19  =  350

Divide the sum by the number of students.

350 ÷ 12  ≈  29.2

Step 4 :

Calculate the mean absolute deviation for the numbers of minutes playing video games.

 |13-29.2|  =  16.2 |18-29.2|  =  11.2 |19-29.2|  =  10.2|30-29.2|  =  0.8 |32-29.2|  =  2.8 |46-29.2|  =  16.8 |50-29.2|  =  20.8 |34-29.2|  =  4.8 |36-29.2|  =  6.8|30-29.2|  =  0.8 |23-29.2|  =  6.2 |19-29.2|  =  10.2

Find the mean of the absolute values. Round to the nearest tenth.

16.2 + 11.2 + 10.2 + 0.8 + 2.8 + 16.8 + 20.8 + 4.8 + 6.8 + 0.8 + 6.2 + 10.2  =  107.6

Divide the sum by the number of students.

107.6 ÷ 12  ≈  9

Step 5 :

Find the difference in the means.

Subtract the lesser mean from the greater mean.

29.2 - 17  =  12.2

Step 6 :

Write the difference of the means as a multiple of the mean absolute deviations, which are similar but not identical.

Divide the difference of the means by the MAD.

12.2 ÷ 9  ≈  1.36

The means of the two data sets differ by about 1.4 times the variability of the two data sets.

## Comparing differences in centers to variability - Practice question

Question :

The high jumps in inches of the students on two intramural track and field teams are shown below. What is the difference of the means as a multiple of the mean absolute deviations ?

Solution :

After having gone through the stuff given above, we hope that the students would have understood "Comparing differences in centers to variability".

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

You can also visit the following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6