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Finding the Sample Median. Find the sample median x. ~. Illustration A: An odd number of data. Given : The distance, in feet, run in five seconds by second graders during a fitness evaluation test was recorded as:. 41,. 48,. 27,. 55,. 31,. 45,. 51. Ranking the Data. 3rd. 5th. - PowerPoint PPT Presentation
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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 = { }
smallest3rd 2nd 4th5th 6thlargest
27,1st
31,2nd
41,3rd
45,4th
48,5th
51,6th
557th
smallest3rd 2nd 4th5th 6thlargest
3
The Formula
Ranked data = { 27, 31, 41, 45, 48, 51, 55 }
1 2 3 4 5 6 71 2 3 4 5 6 7
= +1
2=
82
= 4
n = 77
Next, the depth (position from end) of the median, d (x), is determined using the formula:
~
d(x) =n+1
2~
77
7
d (x) = 4~d(x) =n+1
2~ n
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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
Position1
Position2
Position3
Position4
Position4
Position3
Position2
Position1
Fromthe smallest value data
Fromthe 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
Position1
Position2
Position3
Position4
Position4
Position3
Position2
Position1
Fromthe smallest value data
Fromthe 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
6th3rdSmallest 4th 2nd5th 7thLargest
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
Smallest 4th 2nd5th 7thLargest
8, 3rd
11,6th
3rd 6th
8
88
1 2 3 4 5 6 7 8
The Formula
Ranked data = { 6, 8, 8, 10, 11, 11, 12, 13}
= +1
2=
92
= 4.5
n = 8881 2 3 4 5 6 7 8
Next, the depth (position from end) of the median, d (x), is determined using the formula:
~
d(x) =n+1
2~
d(x) =n+1
2~ n
d (x) = 4.5~
9
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Determining the Median Value
Position1
Position2
Position3
Position4
=212
= 10.5 = 10.5x~x~ =2+
Fromthe smallest value data
Ranked data = {6, 8, 8, 10, 11, 11, 12, 13}
Position5
10 11
1110+11
d (x) = 4.5~
~ The .5 part of d(x) indicates the median value is half way between the values of the data in the4th and 5th positions of the ranked data:
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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:
Position1
Position2
Position3
Position4
Fromthe smallest value data
Ranked data = {6, 8, 8, 10, 11, 11, 12, 13}
Position5
Position4
Position3
Position2
Position1
Fromthe largest value data
Position5
Notice that the same two data are located from either end
