Understanding Central Tendency Measures in Statistics
Learn how to calculate central tendency measures such as mean, median, and mode to analyze data effectively. Explore examples and explanations to grasp the concept easily.
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Presentation Transcript
Central Tendency Measures Central Tendency Measures
Example1 : Find the central tendency measures from the data below: 19 ,15, 22, 17, 21, 17 , 25 , 18 , 17 . Solution : ? 1- The Mean is ( ? ) = ?=1 ?? ? 9= 19 ? = 19+15+ +17 = 171 9 2- To find the Median we have to arrange data from least to greatest 15 , 17, 17, 17, 18 , 19 ,21 , 22, 25 Because there is an odd number of scores , the median is the middle number. It is ??= 18
If we have the raw data as : 19 ,15, 22, 17, 21, 17 , 25 , 18 , 17 , 20 Because there is an even number of scores , the median is the average number of the middle scores . 15 , 17, 17, 17, 18 , 19 ,20 , 21 , 22, 25 So that the average is = 18+19 = 18.5 = Median. 2 3- The mode is the number occurs most frequently. 15 , 17, 17, 17, 18 , 19 , 21 , 22, 25 17 there is one mode.
For example, if you multiply three numbers, the geometric mean is the third root of the product of those three numbers. The geometric mean of five numbers is the fifth root of their product. Suppose we said we found the geometric mean using the 11th11th root of the numbers. That tells you that 11 numbers were multiplied together. To find the geometric mean of four numbers, what root would we take? The fourth root, of course.
Example: from the data find the arithmetic mean Classes Frequency Mid Class 50 - 55 3 52.5 56 - 61 3 58.5 62 - 67 2 64.5 68 - 73 3 70.5 74 - 79 2 76.5 Total 13
? ( ) = ?=1 ???? =?1?1+ ?2?2+ + ???? ? ? =826.5 13 = 3(52.5)+3(58.5)+ +2(76.5) =63.58 13
Example 2: A group of planners measured the length of road (to the nearest km) and group the results: Length (Km) Frequency 150 - 154 5 155 - 159 2 160 - 164 6 165 - 169 8 170 - 174 9 175 - 179 11 180 - 184 6 185 - 189 Total 3 50
Midpoint x Frequency f Length (km) f x 760 150 - 154 152 5 314 155 - 159 157 2 ? ( ) = ?=1 ???? ? 972 160 - 164 162 6 1336 165 - 169 167 8 Mean = 8530 1548 170 - 174 172 9 = 170.6 Km 50 1947 175 - 179 177 11 1092 180 - 184 182 6 561 185 - 189 187 3 8530 Totals 50
