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Data Analysis (Dot/Box/Stem Plots and Histograms)
Histograms
Five Number Summary (Min, Q1, Median, Q3, Max)
Example: { 7 , 6 , 3 , 2 , 10 , 12 , 5 , 5 }
First, count the terms. (n=8)
Second, re-write the set in least-to-greatest order.
{ 2 , 3 , 5 , 5 , 6 , 7, 10 , 12 }
Third, identify the MIN (smallest) = 2 and the MAX (largest) = 12
Fourth, calculate the median. Since n is even, you will have to average the two "middle" numbers.
MEDIAN = (5+6)/2 = 11/2 = 5.5
Fifth, calculate the Q1 by finding the "median" of the first half of the data { 2 , 3 , 5 , 5 }
Q1 = (3+5)/2 = 8/2 = 4
Sixth, calculate the Q3 by finding the "median" of the second half of the data { 6 , 7 , 10 , 12 }
Q3 = (7+10)/2 = 17/2 = 8.5
MIN = 2
Q1 = 4
MED = 5.5
Q3 = 8.5
MAX = 12
______________________________
Example: { 41 , 20 , 3 , 16 , 22 , 38 , 19 , 5 , 35 , 11 , 9 }
First, count the terms. (n=11)
Second, re-write the set in least-to-greatest order.
{ 3 , 5 , 9 , 11 , 16 , 19 , 20 , 22 , 35 , 38 , 41 }
Third, identify the MIN (smallest) = 3 and the MAX (largest) = 41
Fourth, calculate the median. Since n is odd, you will have to find the exact middle number
MEDIAN = 19
Fifth, calculate the Q1 by finding the "median" of the first half of the data (without the median) { 3 , 5 , 9 , 11 , 16 }
Q1 = 9
Sixth, calculate the Q3 by finding the "median" of the second half of the data (without the median) { 20 , 22 , 35 , 38 , 41 }
Q3 = 35
MIN = 3
Q1 = 9
MED = 19
Q3 = 35
MAX = 41
First, count the terms. (n=8)
Second, re-write the set in least-to-greatest order.
{ 2 , 3 , 5 , 5 , 6 , 7, 10 , 12 }
Third, identify the MIN (smallest) = 2 and the MAX (largest) = 12
Fourth, calculate the median. Since n is even, you will have to average the two "middle" numbers.
MEDIAN = (5+6)/2 = 11/2 = 5.5
Fifth, calculate the Q1 by finding the "median" of the first half of the data { 2 , 3 , 5 , 5 }
Q1 = (3+5)/2 = 8/2 = 4
Sixth, calculate the Q3 by finding the "median" of the second half of the data { 6 , 7 , 10 , 12 }
Q3 = (7+10)/2 = 17/2 = 8.5
MIN = 2
Q1 = 4
MED = 5.5
Q3 = 8.5
MAX = 12
______________________________
Example: { 41 , 20 , 3 , 16 , 22 , 38 , 19 , 5 , 35 , 11 , 9 }
First, count the terms. (n=11)
Second, re-write the set in least-to-greatest order.
{ 3 , 5 , 9 , 11 , 16 , 19 , 20 , 22 , 35 , 38 , 41 }
Third, identify the MIN (smallest) = 3 and the MAX (largest) = 41
Fourth, calculate the median. Since n is odd, you will have to find the exact middle number
MEDIAN = 19
Fifth, calculate the Q1 by finding the "median" of the first half of the data (without the median) { 3 , 5 , 9 , 11 , 16 }
Q1 = 9
Sixth, calculate the Q3 by finding the "median" of the second half of the data (without the median) { 20 , 22 , 35 , 38 , 41 }
Q3 = 35
MIN = 3
Q1 = 9
MED = 19
Q3 = 35
MAX = 41
Range and Interquartile Range (IQR)
RANGE = MAX - MIN
IQR = Q3 - Q1
Example:
MIN = 2
Q1 = 4
MED = 5.5
Q3 = 8.5
MAX = 12
Range = Max - Min = 12 - 2 = 10
IQR = Q3 - Q1 = 8.5 - 4 = 4.5
Example:
MIN = 3
Q1 = 9
MED = 19
Q3 = 35
MAX = 41
Range = Max - Min = 41- 3 = 38
IQR = Q3 - Q1 = 35 - 9 = 26
IQR = Q3 - Q1
Example:
MIN = 2
Q1 = 4
MED = 5.5
Q3 = 8.5
MAX = 12
Range = Max - Min = 12 - 2 = 10
IQR = Q3 - Q1 = 8.5 - 4 = 4.5
Example:
MIN = 3
Q1 = 9
MED = 19
Q3 = 35
MAX = 41
Range = Max - Min = 41- 3 = 38
IQR = Q3 - Q1 = 35 - 9 = 26
Box and Whisker Plots
In the box and whisker plot above...
MIN = 11
Q1 = 14
MED = 16
Q3 = 20
MAX = 25
and thus...
RANGE = 15
IQR = 6
MIN = 11
Q1 = 14
MED = 16
Q3 = 20
MAX = 25
and thus...
RANGE = 15
IQR = 6