Lecture number 3 data description 23 99 measures of

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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
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Measures of Central Tendecny - The Median
From examples 5 and 6, we note the following about the median:
(1) When there are an odd number of measurements, the median will be
an actual data value.
(2) The median for an even number of measurements is the average of the
two middle values when the measurements are arranged from lowest to
highest.
(3) Thus, whether there are an even or odd number of measurements, there
are an equal number of measurements above and below the median.
Note also that: The value 0 . 5( n + 1) indicates the position of the
median in the ordered data set. If the position of the median is a
number that ends in the value .5, you need to average the two
adjacent values.
The advantage of using the median as centre of the distribution is
that it is affected less than the mean by extremely high or extremely
low values.- consider example 4.
The median for example 4 is 15 even if the seventh observation is 30,
202 or 2002!
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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.
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