Mean Deviation or Average Deviation

I spoke about positional measures in my previous post Measures of dispersion – Range, Quartile Deviation.

Mean Deviation

Let’s discuss about Mean Deviation, which is the arithmetic mean of the deviations of a data series computed from any measure of central tendency.

Mean Deviation = Σ |D| / N

Σ |D| is the total of all deviations and N is the number of samples.

Mean deviation is calculated by any measure of central tendency as an absolute value.

Coefficient of Mean Deviation

Coefficient of mean deviation is obtained by dividing the mean deviation by the average used for calculating the mean deviation.

How to calculate Mean Deviation?

  1. Calculate the mean, median or mode of the data series
  2. Take a deviation of items from average, ignoring the + – signs. Mark these deviations using |D|
  3. Compute the total of these deviations to get Σ |D|
  4. Divide the total by number of items.

Data set:

100, 150, 200, 250, 360, 490, 500, 600, 671

X |D| = x-x̄ |D| = X-Median
100 269 (360-100) 260 (360 – 100)
150 219 210
200 169 160
250 119 110
360 9 0
490 121 130
500 131 140
600 231 240
671 302 311
ΣX = 3321

Average or Mean is 3321/9 = 369

Median is 360

Σ |D| = 1570 Σ |D| = 1561

Mean Deviation from the mean = Σ |D|/N = 1570/9 = 174.44

Coefficient of mean deviation = Mean Deviation/Average Mean = 174.4/369 = 0.47

Mean Deviation from the median = Σ |D|/N  =1561/9 = 173.44

Coefficient of median deviation = Median deviation/Median = 173.44/360 = 0.48

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Measures of Central Tendency

A measure of central tendency gives us an idea about where the middle of the data lies.

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We shall discuss about the following in this post.

  • Mean
  • Median
  • Mode

Mean

  • It shall be used against discrete and continuous data
  • This is equal to the sum of all values divided by the number of data
  • Usually it is represented by x-bar x̄.

x̄ = Σx/n

Lets take the following example to explain mean. Here is the data about the length of the runways in commercial airports of Tamil Nadu.

Airport Runway length in meters
Chennai – I 3,658
Chennai – II 2,925
Trichy 2,480
Madurai 2,285
Coimbatore 3,120
Tuticorin 1,351
Salem 1,806

Hence the mean length of runways

x̄  or μ = 3568+2925+2480+2285+3120+1351+1806 / 7
μ = 17,625/7
μ = 2518 meters!

You may use average function in Excel – =AVERAGE(D2:D8).

Median

When we sort the data in any order, the items found in the middle is called median.

Lets take the same example in ascending order.

Airport Runway length in meters Average
Tuticorin 1,351 2,518
Salem 1,806 2,518
Madurai 2,285 2,518
Trichy 2,480 2,518
Chennai – II 2,925 2,518
Coimbatore 3,120 2,518
Chennai – I 3,658 2,518

So 1351, 1806, 2285, 2480, 2925, 3120, 3658 we have 7 data. Lets take the data in the middle, which is 2480, which is our median.

If we have even number of samples, average of middle values is the median.

Excel function: =MEDIAN(D2:D8)

Mode

The observation data observed frequently in the population is called mode. Let’s modify the above given data slightly to explain mode.

Airport Runway length in meters
Tuticorin 1,000
Salem 2,000
Madurai 2,000
Trichy 2,000
Chennai – II 3,000
Coimbatore 3,000
Chennai – I 4,000

2000 is repeated thrice. Hence this is the mode of this data set.

Excel function: =MODE.SNGL(E2:E8)