Median

Transcript

MedianWhen outliers mess up the average, we use the Median. The Median is simply the middle number when the data is sorted. How to find the Median? SORT the numbers from smallest to largest. Pick the number in the exact middle. Special Rule: If there are two numbers in the middle (because you have an even number of items), you take the average of those two. Now, let’s find median for the Height question The heights of the family members of Yaangba and Poovizhi are as follows: Yaangba’s family: 169 cm, 173 cm, 155 cm, 165 cm, 160 cm, 164 cm. Poovizhi’s family: 170 cm, 173 cm, 165 cm, 118 cm, 175 cm. Find the median for each We do this one-by-one Yaangba’s family Height given are 169 cm, 173 cm, 155 cm, 165 cm, 160 cm, 164 cm. First, we write it in ascending order (we can do descending order also) 155 cm, 160 cm, 164 cm, 165 cm, 169 cm, 173 cm Number of observations = 6 Since number of observations is even, We use the average of the two middle numbers Our middle numbers are 164 cm & 165 cm Thus, Median = (164 + 165)/2 = 329/2 = 164.5 cm Thus, Median height for Yaangba’s family is 164.5 cm Poovizhi’s family: Height given are 170 cm, 173 cm, 165 cm, 118 cm, 175 cm. First, we write it in ascending order (we can do descending order also) 118 cm, 165 cm, 170 cm, 173 cm, 175 cm Number of observations = 5 Since number of observations is odd, Median is the middle number Thus, Median = 170 cm Thus, Median height for Poovizhi’s family is 170 cm Visualising using Dot Diagram We notice that Median is the middle most value, and represents the heights better than mean