 # 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 # Measures of Central Tendency

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