**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.

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.

**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 :**

About 1.1 times the MAD.

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 above, if you want to know more about "Comparing differences in centers to variability", please click here

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

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**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**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**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 **

**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 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**