Download Measures of Central Tendency

Measures of Central Tendency
Statistics For Business
MATH0201
The arithmetic mean is the best known type of average
and is widely understood. It is used for further statistical
analysis.
“x bar”
Advantages
• widely understood
•It is easy to calculate
•Represents whole set of
data
•Suited to further statistical
analysis
Disadvantages
•Value may not correspond
to an actual value
•Distorted by extreme values
Eg. Mean : ungrouped data
Find arithmetic mean of data in a frequency distribution
= ∑fx / ∑f
x = 185 / 20 = 9.25
Find arithmetic mean of grouped data
• Find mid-point of each class interval.
Arithmetic mean x = ∑ fx / ∑f
= 190 / 20
= 9.5 units
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
The median of ungrouped frequency distribution
remember to arrange the
items in order of value first
The median of a grouped frequency distribution
can be estimated from an ogive
The mode is an average which is the most frequently
occurring value.
Advantages
• easy to find
•Uninfluenced by a few
extreme values
•Can be used for nonnumerical data
Disadvantages
•Does not take every value
into account
•Some instability in the
measure
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.
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(Hm - Hm-) + (Hm - Hm+)
X (U – L)
Eg.
Invoice value (US$) Frequency, f
2 and under 6
6 and under 10
10 and under 14
14 and under 18
18 and under 22
22 and under 30
1
6
6
10
8
9
Frequency density
0.250
1.500
1.500
2.500
2.000
1.125