1 Finding the Sample Median  Given: The distance, in feet, run in five seconds by second graders during a fitness evaluation test was recorded as:  Find the sample median x ~ 41,48,27,55,31,45,51 Illustration A: An odd number of data

2 Ranking the Data  Since the median is the “middle value”, the data must first be ranked in order of value  Typically, ranking is smallest value first and largest value last: (Do you have your sample data ready to use?) Sample data = {41, 48, 27, 55, 31, 45, 51} Ranked data = { } smallest3rd2nd4th5th6th largest 27, 1st 31, 2nd 41, 3rd 45, 4th 48, 5th 51, 6th 55 7th smallest3rd2nd4th5th6thlargest

3 The Formula Ranked data = { 27, 31, 41, 45, 48, 51, 55 } = +1 2 = 8282 = 4 n = 7 7  Next, the depth (position from end) of the median, d (x), is determined using the formula: ~ d(x) =d(x) = n+1 2 ~ d (x) = 4 ~ d(x) =d(x) = n+1 2 ~ n

4 Determining the Median Value  The value of the median is determined by locating the data in the 4th position of the ranked data and observing its value: Ranked data = { } 27,31,41,45,48,51,55 Position 1 Position 2 Position 3 Position 4 Position 4 Position 3 Position 2 Position 1 From the smallest value data From the largest value data  The median can also be determined by locating the data in the 4th position from the largest

5 The Answer! Ranked data = { } 27,31,41,45,48,51,55 Position 1 Position 2 Position 3 Position 4 Position 4 Position 3 Position 2 Position 1 From the smallest value data From the largest value data The median distance is 45 feet  Notice that the same data is located from either end, which means you can find the median one way and use the other as a check

6 Finding the Sample Median  Given: The distance, in feet, ran in five seconds by preschoolers during a fitness evaluation test was recorded as:  Find the sample median x ~ 6,10,13,11,12,8, Illustration B: An even number of data 8,11

7 6th3rd Smallest 4th2nd5th7th Largest Ranking the Data  Since the median is the “middle value”, the data must first be ranked in order of value  Typically, ranking is smallest value first and largest value last: (Do you have your sample data ready to use?) Sample data = {6, 10, 13, 11, 12, 8, 8, 11} Ranked data = { } 6, 1st 8, 2nd 10, 4th 11, 5th 12, 7th 13 8th Smallest4th2nd5th7thLargest 8, 3rd 11, 6th 3rd6th

The Formula Ranked data = { 6, 8, 8, 10, 11, 11, 12, 13} = +1 2 = 9292 = 4.5 n =  Next, the depth (position from end) of the median, d (x), is determined using the formula: ~ d(x) =d(x) = n+1 2 ~ d(x) =d(x) = n+1 2 ~ n d (x) = 4.5 ~

9 10 Determining the Median Value Position 1 Position 2 Position 3 Position 4 = 21 2 = 10.5 x ~ x ~ = 2 + From the smallest value data Ranked data = {6, 8, 8, 10, 11, 11, 12, 13} Position d (x) = 4.5 ~ ~  The.5 part of d(x) indicates the median value is half way between the values of the data in the 4th and 5th positions of the ranked data:

10 The Answer! The median distance is 10.5 feet  As before, the median can also be determined by locating the data in the 4.5th position from the largest: Position 1 Position 2 Position 3 Position 4 From the smallest value data Ranked data = {6, 8, 8, 10, 11, 11, 12, 13} Position 5 Position 4 Position 3 Position 2 Position 1 From the largest value data Position 5  Notice that the same two data are located from either end