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

Statistics at HelpWithAssignment.com (Hypothesis Testing)

Hypothesis is making an assumption. In Statistics, a Hypothesis or an assumption is taken first and then the Hypothesis is tested whether it is accurate or not. Hypothesis testing is a study based on statistical accuracy of an experiment. If the result is positive, then it is called statistically significant.
There are two types of statistical hypotheses. A Null Hypothesis and an Alternate Hypothesis. A Null Hypothesis is denoted by H0, it is actually an assumption that the simple observations are purely from chance.
Alternate Hypothesis on the other hand is denoted by H1 or Ha, assumes that that sample is influenced by a non-random cause.
An example for Hypothesis Testing.
Suppose that we want to test the hypothesis with a significance level of .05 that the climate has changed since industrialization. Suppose that the mean temperature throughout history is 50 degrees. During the last 40 years, the mean temperature has been 51 degrees and suppose the population standard deviation is 2 degrees. What can we conclude?
We have
H0: µ = 50 or the temperature is normal
H1: µ ≠50 or the temperature has changed
We compute the z score:
(51-50)/(2/√40) = 3.16
The table gives us 0.9992
So that p = (1 – 0.9992)(2) = 0.002
Since 0.002 <0.05 We can conclude that the Alternate Hypothesis is accepted and there has been a change in temperature.

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This article is in continuation with our previous articles on Statistics Regression and Statistics Correlation