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Calculation of Quartiles by TI Calculator
Calculation of QuartilesFormula Used by TI Calculator
J.C. Wang
JC Wang (WMU) Stat2160 S2160 1 / 9
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Calculation of Quartiles by TI Calculator
Outline
1 Calculation of Quartiles by TI CalculatorFormula
Examples
JC Wang (WMU) Stat2160 S2160 2 / 9
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Calculation of Quartiles by TI Calculator
Outline
1 Calculation of Quartiles by TI CalculatorFormula
Examples
JC Wang (WMU) Stat2160 S2160 3 / 9
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Calculation of Quartiles by TI Calculator
Formulafor Quartile Calculation
TI calculator usemedian of lower half data values (before MED) for first quartile
median of upper half data values (after MED) for third quartile
JC Wang (WMU) Stat2160 S2160 4 / 9
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Calculation of Quartiles by TI Calculator
Formulafor Quartile Calculation
TI calculator usemedian of lower half data values (before MED) for first quartile
median of upper half data values (after MED) for third quartile
JC Wang (WMU) Stat2160 S2160 4 / 9
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Calculation of Quartiles by TI Calculator
Formulacontinued
Denote ordered data values (in ascending order):
x(1), x(2), . . . , x(n)
for even sample size n, (note: MED = [x(n/2) + x(n/2+1)]/2)
Q1 = median of x(1), . . . , x(n/2)
Q3 = median of x(n/2+1), . . . , x(n)
for odd sample size n, (note: MED = x((n+1)/2))
Q1 = median of x(1), . . . , x((n+1)/21)
Q3 = median of x((n+1)/2+1), . . . , x(n)
JC Wang (WMU) Stat2160 S2160 5 / 9
C Q C
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Calculation of Quartiles by TI Calculator
Formulacontinued
Denote ordered data values (in ascending order):
x(1), x(2), . . . , x(n)
for even sample size n, (note: MED = [x(n/2) + x(n/2+1)]/2)
Q1 = median of x(1), . . . , x(n/2)
Q3 = median of x(n/2+1), . . . , x(n)
for odd sample size n, (note: MED = x((n+1)/2))
Q1 = median of x(1), . . . , x((n+1)/21)
Q3 = median of x((n+1)/2+1), . . . , x(n)
JC Wang (WMU) Stat2160 S2160 5 / 9
C l l ti f Q til b TI C l l t
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Calculation of Quartiles by TI Calculator
Even Sample Size Data SetSummer II Quiz Example
n = 14
8 11 13 19 21 23 25
25 25 28 31 35 39 47
Lower half of the data set has 7 (an odd number) values:
7 + 1
2= 4
JC Wang (WMU) Stat2160 S2160 6 / 9
Calculation of Quartiles by TI Calculator
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Calculation of Quartiles by TI Calculator
Even Sample Size Data SetSummer II Quiz Example
n = 14
8 11 13 19 21 23 25
25 25 28 31 35 39 47
Lower half of the data set has 7 (an odd number) values:
7 + 1
2= 4
JC Wang (WMU) Stat2160 S2160 6 / 9
Calculation of Quartiles by TI Calculator
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Calculation of Quartiles by TI Calculator
Even Sample Size Data SetSummer II Quiz Example
n = 14
8 11 13 19 21 23 25
25 25 28 31 35 39 47
Lower half of the data set has 7 (an odd number) values:
7 + 1
2= 4
Hence
Q1 = 4th ordered value from low end = 19
JC Wang (WMU) Stat2160 S2160 6 / 9
Calculation of Quartiles by TI Calculator
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Calculation of Quartiles by TI Calculator
Even Sample Size Data SetSummer II Quiz Example
n = 14
8 11 13 19 21 23 25
25 25 28 31 35 39 47
Lower half of the data set has 7 (an odd number) values:
7 + 1
2= 4
Hence
Q1 = 4th ordered value from low end = 19
Q3 = 4th ordered value from high end = 31
JC Wang (WMU) Stat2160 S2160 6 / 9
Calculation of Quartiles by TI Calculator
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Calculation of Quartiles by TI Calculator
Even Sample Size Data SetSummer II Quiz Example
n = 14
8 11 13 19 21 23 25
25 25 28 31 35 39 47
Lower half of the data set has 7 (an odd number) values:
7 + 1
2= 4
Hence
Q1 = 4th ordered value from low end = 19
Q3 = 4th ordered value from high end = 31
JC Wang (WMU) Stat2160 S2160 6 / 9
Calculation of Quartiles by TI Calculator
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Calculation of Quartiles by TI Calculator
Even Sample Size Data SetProblem 5, page 40
n = 12
1.9 2.2 11.2 13.5 14.4 17.0
21.8 23.8 28.4 32.6 38.0 41.4
Lower half of the data set has 6 (an even number) values
JC Wang (WMU) Stat2160 S2160 7 / 9
Calculation of Quartiles by TI Calculator
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y
Even Sample Size Data SetProblem 5, page 40
n = 12
1.9 2.2 11.2 13.5 14.4 17.0
21.8 23.8 28.4 32.6 38.0 41.4
Lower half of the data set has 6 (an even number) values
JC Wang (WMU) Stat2160 S2160 7 / 9
Calculation of Quartiles by TI Calculator
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y
Even Sample Size Data SetProblem 5, page 40
n = 12
1.9 2.2 11.2 13.5 14.4 17.0
21.8 23.8 28.4 32.6 38.0 41.4
Lower half of the data set has 6 (an even number) values
Q1 = average of 3rd & 4th order values from low end
=11.2 + 13.5
2
= 12.35
JC Wang (WMU) Stat2160 S2160 7 / 9
Calculation of Quartiles by TI Calculator
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Even Sample Size Data SetProblem 5, page 40
n = 12
1.9 2.2 11.2 13.5 14.4 17.0
21.8 23.8 28.4 32.6 38.0 41.4
Lower half of the data set has 6 (an even number) values
Q1 = average of 3rd & 4th order values from low end
=11.2 + 13.5
2
= 12.35
Q3 = average of 3rd & 4th order values from high end
=28.4 + 32.6
2= 30.5
JC Wang (WMU) Stat2160 S2160 7 / 9
Calculation of Quartiles by TI Calculator
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Even Sample Size Data SetProblem 5, page 40
n = 12
1.9 2.2 11.2 13.5 14.4 17.0
21.8 23.8 28.4 32.6 38.0 41.4
Lower half of the data set has 6 (an even number) values
Q1 = average of 3rd & 4th order values from low end
=11.2 + 13.5
2
= 12.35
Q3 = average of 3rd & 4th order values from high end
=28.4 + 32.6
2= 30.5
JC Wang (WMU) Stat2160 S2160 7 / 9
Calculation of Quartiles by TI Calculator
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Odd Sample Size Data SetPharmacia Stock Data, page 32
n = 2139.60 40.52 40.56 42.65 44.40 44.62 45.95 48.56 49.93 50.37
51.68
51.70 51.93 52.26 54.75 55.00 56.02 58.56 60.18 61.00 61.00
Lower half of the data set has 10 (an even number) values
JC Wang (WMU) Stat2160 S2160 8 / 9
Calculation of Quartiles by TI Calculator
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Odd Sample Size Data SetPharmacia Stock Data, page 32
n = 2139.60 40.52 40.56 42.65 44.40 44.62 45.95 48.56 49.93 50.37
51.68
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Odd Sample Size Data SetPharmacia Stock Data, page 32
n = 2139.60 40.52 40.56 42.65 44.40 44.62 45.95 48.56 49.93 50.37
51.68
51.70 51.93 52.26 54.75 55.00 56.02 58.56 60.18 61.00 61.00
Lower half of the data set has 10 (an even number) values
Q1 = average of 5th & 6th order values from low end
=44.40 + 44.62
2= 44.51
JC Wang (WMU) Stat2160 S2160 8 / 9
Calculation of Quartiles by TI Calculator
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Odd Sample Size Data SetPharmacia Stock Data, page 32
n = 2139.60 40.52 40.56 42.65 44.40 44.62 45.95 48.56 49.93 50.37
51.68
51.70 51.93 52.26 54.75 55.00 56.02 58.56 60.18 61.00 61.00
Lower half of the data set has 10 (an even number) values
Q1 = average of 5th & 6th order values from low end
=44.40 + 44.62
2= 44.51
Q3 = average of 5th & 6th order values from high end
=55.00 + 56.02
2= 55.51
JC Wang (WMU) Stat2160 S2160 8 / 9
Calculation of Quartiles by TI Calculator
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Odd Sample Size Data SetPharmacia Stock Data, page 32
n = 2139.60 40.52 40.56 42.65 44.40 44.62 45.95 48.56 49.93 50.37
51.68
51.70 51.93 52.26 54.75 55.00 56.02 58.56 60.18 61.00 61.00
Lower half of the data set has 10 (an even number) values
Q1 = average of 5th & 6th order values from low end
=44.40 + 44.62
2= 44.51
Q3 = average of 5th & 6th order values from high end
=55.00 + 56.02
2= 55.51
JC Wang (WMU) Stat2160 S2160 8 / 9
Calculation of Quartiles by TI Calculator
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Odd Sample Size Data SetApartment Rental Data, page 39
n = 15
550 560 575 600 625 625 650
675
700 725 740 750 775 850 1100
Lower half of the data set has 7 (an odd number) values:7+1
2 = 4
JC Wang (WMU) Stat2160 S2160 9 / 9
Calculation of Quartiles by TI Calculator
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Odd Sample Size Data SetApartment Rental Data, page 39
n = 15
550 560 575 600 625 625 650
675
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Odd Sample Size Data SetApartment Rental Data, page 39
n = 15
550 560 575 600 625 625 650
675
700 725 740 750 775 850 1100
Lower half of the data set has 7 (an odd number) values:7+1
2 = 4
Q1 = 4th order value from low end = 600
JC Wang (WMU) Stat2160 S2160 9 / 9
Calculation of Quartiles by TI Calculator
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Odd Sample Size Data SetApartment Rental Data, page 39
n = 15
550 560 575 600 625 625 650
675
700 725 740 750 775 850 1100
Lower half of the data set has 7 (an odd number) values:7+1
2 = 4
Q1 = 4th order value from low end = 600
Q3 = 4th order value from high end = 750
JC Wang (WMU) Stat2160 S2160 9 / 9
Calculation of Quartiles by TI Calculator
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Odd Sample Size Data SetApartment Rental Data, page 39
n = 15
550 560 575 600 625 625 650
675
700 725 740 750 775 850 1100
Lower half of the data set has 7 (an odd number) values:7+1
2 = 4
Q1 = 4th order value from low end = 600
Q3 = 4th order value from high end = 750
JC Wang (WMU) Stat2160 S2160 9 / 9