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)

 

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2 thoughts on “Measures of Central Tendency

  1. Pingback: Measures of dispersion – Range, Quartile Deviation | JavaShine

  2. Pingback: Mean Deviation or Average Deviation | JavaShine

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