Lecture Number 3 Data Description 23 99 Measures of Central

Lecture number 3 data description 23 99 measures of

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Lecture Number 3 Data Description October 19, 2016 23 / 99
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 Data Description October 19, 2016 24 / 99
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 Data Description October 19, 2016 25 / 99
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 Data Description October 19, 2016 26 / 99

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