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Measures of Central Tendency Statistics For Business MATH0201

Measures of Central Tendency - FTMS...Measures of Central Tendency Author: Nurazrin Created Date: 12/21/2012 4:29:56 PM

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Page 1: Measures of Central Tendency - FTMS...Measures of Central Tendency Author: Nurazrin Created Date: 12/21/2012 4:29:56 PM

Measures of Central Tendency Statistics For Business

MATH0201

Page 2: Measures of Central Tendency - FTMS...Measures of Central Tendency Author: Nurazrin Created Date: 12/21/2012 4:29:56 PM

“x bar”

The arithmetic mean is the best known type of average and is widely understood. It is used for further statistical analysis.

Page 3: Measures of Central Tendency - FTMS...Measures of Central Tendency Author: Nurazrin Created Date: 12/21/2012 4:29:56 PM

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

Page 4: Measures of Central Tendency - FTMS...Measures of Central Tendency Author: Nurazrin Created Date: 12/21/2012 4:29:56 PM

Eg. Mean : ungrouped data

Page 5: Measures of Central Tendency - FTMS...Measures of Central Tendency Author: Nurazrin Created Date: 12/21/2012 4:29:56 PM

Find arithmetic mean of data in a frequency distribution

x = 185 / 20 = 9.25 = ∑fx / ∑f

Page 6: Measures of Central Tendency - FTMS...Measures of Central Tendency Author: Nurazrin Created Date: 12/21/2012 4:29:56 PM

Find arithmetic mean of grouped data

• Find mid-point of each class interval.

Arithmetic mean x = ∑ fx / ∑f = 190 / 20 = 9.5 units

Page 7: Measures of Central Tendency - FTMS...Measures of Central Tendency Author: Nurazrin Created Date: 12/21/2012 4:29:56 PM

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

Page 8: Measures of Central Tendency - FTMS...Measures of Central Tendency Author: Nurazrin Created Date: 12/21/2012 4:29:56 PM

The median of ungrouped frequency distribution

remember to arrange the items in order of value first

Page 9: Measures of Central Tendency - FTMS...Measures of Central Tendency Author: Nurazrin Created Date: 12/21/2012 4:29:56 PM

The median of a grouped frequency distribution

can be estimated from an ogive

Page 10: Measures of Central Tendency - FTMS...Measures of Central Tendency Author: Nurazrin Created Date: 12/21/2012 4:29:56 PM

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

Page 11: Measures of Central Tendency - FTMS...Measures of Central Tendency Author: Nurazrin Created Date: 12/21/2012 4:29:56 PM

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.

Page 12: Measures of Central Tendency - FTMS...Measures of Central Tendency Author: Nurazrin Created Date: 12/21/2012 4:29:56 PM

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+)

Page 13: Measures of Central Tendency - FTMS...Measures of Central Tendency Author: Nurazrin Created Date: 12/21/2012 4:29:56 PM

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

Page 14: Measures of Central Tendency - FTMS...Measures of Central Tendency Author: Nurazrin Created Date: 12/21/2012 4:29:56 PM