measures of central tendency - ftms...measures of central tendency author: nurazrin created date:...
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Measures of Central Tendency Statistics For Business
MATH0201
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“x bar”
The arithmetic mean is the best known type of average and is widely understood. It is used for further statistical analysis.
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Advantages Disadvantages
• widely understood •It is easy to calculate •Represents whole set of data •Suited to further statistical analysis
•Value may not correspond to an actual value •Distorted by extreme values
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Eg. Mean : ungrouped data
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Find arithmetic mean of data in a frequency distribution
x = 185 / 20 = 9.25 = ∑fx / ∑f
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Find arithmetic mean of grouped data
• Find mid-point of each class interval.
Arithmetic mean x = ∑ fx / ∑f = 190 / 20 = 9.5 units
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The median is the value of the middle item of a distribution once all of the items have been arranged in order of magnitude.
• The median of the following nine values:
8 6 9 12 15 6 3 20 11
• The median of the following ten values:
8 6 9 12 15 6 3 20 11 7
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The median of ungrouped frequency distribution
remember to arrange the items in order of value first
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The median of a grouped frequency distribution
can be estimated from an ogive
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The mode is an average which is the most frequently occurring value.
Advantages Disadvantages
• easy to find •Uninfluenced by a few extreme values •Can be used for non-numerical data
•Does not take every value into account •Some instability in the measure
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The mode of a grouped frequency distribution can be estimated from a histogram Modal class of a histogram is always the class with the tallest bar.
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Graphical method: using formula
Let L be the lower class boundary of the model class U be the upper class boundary of the modal class Hm be the height of the tallest histogram block Hm- be the height of the block before the tallest one Hm+be the height of the block following the tallest one
Then the mode is given by the formula: Mode = L + Hm - Hm- X (U – L) (Hm - Hm-) + (Hm - Hm+)
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Eg.
Invoice value (US$) Frequency, f Frequency density
2 and under 6 1 0.250 6 and under 10 6 1.500 10 and under 14 6 1.500 14 and under 18 10 2.500 18 and under 22 8 2.000 22 and under 30 9 1.125
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