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Probability and Statistics
Lecture 04

Learning Outcomes
• Explain the difference between measures of dispersion and
measures of central tendency
...

• Explains and evaluates various measures of central tendency
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Central Tendency
Central tendency is a descriptive summary of a dataset through a single value
that reflects the center of the data distribution
...

Along with the dispersion, central tendency is a branch of descriptive statistics

Measures of Central Tendencies
•

The mean or the arithmetic average is the most commonly used measure of
central tendency, but there are others, such as the median and the mode
...

• For example, the mean of discrete data 5, 7, 12, 6, and 13 is found by

𝟓 + 𝟕 + 𝟏𝟐 + 𝟔 + 𝟏𝟑 𝟒𝟑
=
= 𝟖
...

• If a dataset contains an even number of values, the median of the dataset
is the mean of the two middle values
...
e
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• It represents the highest bar in a bar chart or histogram
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e
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• For the Following Data Set

46

11

42

35

42

82

65

11

22

36

29

• 11 and 42 are both repeated twice i
...
the most times in the data set
therefore the MODE = 11 and 42, and data set is bimodal

Mode of Ungrouped Data:

Quartiles:
From the definition of median that it is the middle point in the axis frequency
distribution curve, and it divides the area under the curve into two such parts that
it has same area in the left, as in the right
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D1 = 1st Decile
D2 = 2nd Decile

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D5 = 5th Decile = Median

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=A10

Percentile
Finally, if we divide the area into hundred equal pieces then it will be called
percentiles
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Find the median

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=A100

Range:

The difference between the largest and smallest values of a distribution
Range = Max Value – Min Value
Inter Quartile Range

The interquartile range (IQR) is the difference between the first and third quartiles
...
A small interquartile range means
that the data in the middle of the set are close in value
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Mean Absolute Deviation

MAD 

 xx
N



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