Lecture Number 3
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October 19, 2016
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Measures of Central Tendecny  The Median
Solution for Example 5
Step 1.
Arrange the data in ascending order.
2, 5, 6, 9, 11
Step 2.
Select the middle value.
For the data set above, the middle value
is 6. Thus, the median (
m
) is 6.
Example 6
Find the median for the set of measurements 2, 9, 11, 5, 6, 27.
Solution for Example 6
Step 1.
Arrange the data in ascending order. We have: 2, 5, 6, 9, 11, 27
Step 2.
Select the middle value.
Since the middle point or value falls
halfway between 6 and 9, find the median by adding the two values and
dividing by 2. Thus, the median is:
m
=
6+9
2
= 7
.
5
Lecture Number 3
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October 19, 2016
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Measures of Central Tendecny  The MedianFrom examples 5 and 6, we note the following about the median:(1)When there are an odd number of measurements, the median will bean actual data value.(2)The median for an even number of measurements is the average of thetwo middle values when the measurements are arranged from lowest tohighest.(3)Thus, whether there are an even or odd number of measurements, thereare an equal number of measurements above and below the median.Note also that: The value 0.5(n+ 1) indicates the position of themedian in the ordered data set. If the position of the median is anumber that ends in the value .5, you need to average the twoadjacent values.The advantage of using the median as centre of the distribution isthat it is affected less than the mean by extremely high or extremelylow values. consider example 4.The median for example 4 is 15 even if the seventh observation is 30,202 or 2002!
Lecture Number 3
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October 19, 2016
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Measures of Central Tendecny  The Median
The
median for grouped data
is slightly more difficult to compute 
mostly done by extrapolation.
Because the actual values of the measurements are unknown, we
know that the median occurs in a particular class interval, but we do
not know where to locate the median within the interval.
For grouped data, the median is obtained by using the formula:
median
=
L
+
c
f
m
(0
.
5
n

cf
b
)
(4)
where,
L
=lower class boundary of the median class (i.e., the class
containing the median);
c
=the width of the class interval;
f
m
=frequency of median class;
n
=total frequency and
cf
b
=the sum
of frequencies (cumulative frequency) for all classes before the median
class.
Lecture Number 3
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 F. TAILOKA
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