Understanding Central Tendency Properties (Mean, Median and Mode) in Statistics

In Statistics, Measures of Central Tendency are numerical values that locate, in some sense, the centre of a set of data. The term average is often associated with all measures of central tendency.

Mean
1. Measure of central tendency
2. Most common measure
3. Acts as ‘balance point’
4. Affected by extreme values (‘outliers’)
5. Formula (sample mean)

Raw Data: 10.3 4.9 8.9 11.7 6.3 7.7
X = ∑ x/n = x1 + x2 + x3 …..xn /n

Here in this case 10.3+ 4.9+ 8.9 + 11.7 +6.3 + 7.7/6 = 8.3
The mean is 8.3

Median
1. Measure of central tendency
2. Middle value in ordered sequence
• If n is odd, middle value of sequence
• If n is even, average of 2 middle values
3. Position of median in sequence
Positioning Point = n+1/2
4. Not affected by extreme values

Calculating Median from an Odd-sized example
• Raw Data: 24.1 22.6 21.5 23.7 22.6
• Ordered: 21.5 22.6 22.6 23.7 24.1
• Position: 1 2 3 4 5
Positioning Point = n+1/2 = 5+1/2 = 3
Median = 22.6
Median Example from an Even-Sized Sample
• Raw Data: 10.3 4.9 8.9 11.7 6.3 7.7
• Ordered: 4.9 6.3 7.7 8.9 10.3 11.7
• Position: 1 2 3 4 5 6
Positioning Point = n+1/2 = 6+1/2 = 3.5
Median = 7.7 + 8.9/2 = 8.3

Mode
1. Measure of central tendency
2. Value that occurs most often
3. Not affected by extreme values
4. May be no mode or several modes
5. May be used for quantitative or qualitative data

• No Mode
Raw Data: 10.3 4.9 8.9 11.7 6.3 7.7
• One Mode
Raw Data: 6.3 4.9 8.9 6.3 4.9 4.9
• More Than 1 Mode
Raw Data: 21 28 28 41 43 43

Say, if you’re a financial analyst for Prudential-Bache Securities. You have collected the following closing stock prices of new stock issues: 17, 16, 21, 18, 13, 16, 12, 11.
Describe the stock prices in terms of central tendency.

Central Tendency Solution
Mean
X = ∑x/n = 17 + 16 + 21 + 18 + 13 + 16 + 12 + 11/8 = 15.5
Median
• Raw Data: 17 16 21 18 13 16 12 11
• Ordered: 11 12 13 16 16 17 18 21
• Position: 1 2 3 4 5 6 7 8
Positioning Point = n+1/2 = 8+1/2 = 4.5
Median = 16+16/2 = 16
Mode
Raw Data: 17, 16, 21, 18, 13, 16, 12, 11
Mode = 16

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This article is in continuation with our previous article on Statistics (Regression), Statistics (Correlation), Statistics (Hypothesis Testing), Statistics Assignment help