Spreadsheets can be used to find the mean absolute deviation of a data set.

**Example :**

A paper mill is testing two paper-cutting machines. Both are set to produce pieces of paper with a width of 8.5 inches. The actual widths of 8 pieces of paper cut by each machine are shown.

Widths of Pieces of Paper Cut by Machine A (in.) :

8.502, 8.508, 8.499, 8.501, 8.492, 8.511, 8.505, 8.491

Widths of Pieces of Paper Cut by Machine B (in.) :

8.503, 8.501, 8.498, 8.499, 8.498, 8.504, 8.496, 8.502

Use a spreadsheet to determine which machine has less variability and, thus, does a better job.

**Solution :**

**Step 1 : **

Enter the data values for Machine A into row 1 of a spreadsheet, using cells A to H.

**Step 2 : **

Enter “mean = “ into cell A2 and the formula = AVERAGE(A1:H1) into cell B2.

**Step 3 : **

Enter “MAD = “ into cell A3 and the formula = AVEDEV(A1:H1) into cell B3.

The MAD for Machine A is about 0.0054 in.

**Step 4 : **

Repeat Steps 1–3 with the data values for Machine B.

The MAD for Machine B is about 0.0024 in.

Machine B has less variability, so it does a better job.

**Problem :**

The data represent the height, in feet, of various buildings. Find the mean absolute deviation.

60, 58, 54, 56, 63, 65, 62, 59, 56, 57

**Solution :**

Let x = 60, 58, 54, 56, 63, 65, 62, 59, 56, 57

The mean is given by

x̄̄ = (60+58+54+56+63+65+62+59+56+57) / 10

x̄ = 590 / 10

x̄**̄**** = ** 59

Absolute deviations of observations from mean :

|60 - 59 | = |1| = 1

|58 - 59 | = |-1| = 1

|54 - 59 | = |-5| = 5

|56 - 59 | = |-3| = 3

|63 - 59 | = |4| = 4

|65 - 59 | = |6| = 6

|62 - 59 | = |3| = 3

|59 - 59 | = |0| = 0

|56 - 59 | = |-3| = 3

|57 - 59 | = |-2| = 2

Calculate the MAD by finding the mean of the above absolute deviations of observations from mean. Round to the nearest whole number.

MAD = (1 + 1 + 5 + 3 + 4 + 6 + 3 + 0 + 3 + 2) / 10

MAD = 28 / 10

MAD = 2.8 ≈ 3

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

HTML Comment Box is loading comments...

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 **

**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**

**Trigonometry 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**