fivenumsummti.pdf

7/27/2019 FiveNumSummTi.pdf

1/27

Calculation of Quartiles by TI Calculator

Calculation of QuartilesFormula Used by TI Calculator

J.C. Wang

JC Wang (WMU) Stat2160 S2160 1 / 9


2/27


Outline

1 Calculation of Quartiles by TI CalculatorFormula

Examples



3/27


Outline

1 Calculation of Quartiles by TI CalculatorFormula

Examples



4/27


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



5/27


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



6/27


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)


C Q C


7/27


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)


C l l ti f Q til b TI C l l t


8/27


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




9/27



n = 14

8 11 13 19 21 23 25

25 25 28 31 35 39 47


7 + 1

2= 4




10/27



n = 14

8 11 13 19 21 23 25

25 25 28 31 35 39 47


7 + 1

2= 4

Hence

Q1 = 4th ordered value from low end = 19




11/27



n = 14

8 11 13 19 21 23 25

25 25 28 31 35 39 47


7 + 1

2= 4

Hence


Q3 = 4th ordered value from high end = 31




12/27



n = 14

8 11 13 19 21 23 25

25 25 28 31 35 39 47


7 + 1

2= 4

Hence


Q3 = 4th ordered value from high end = 31




13/27


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




14/27

y


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





15/27

y


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


Q1 = average of 3rd & 4th order values from low end

=11.2 + 13.5

2

= 12.35




16/27


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



=11.2 + 13.5

2

= 12.35

Q3 = average of 3rd & 4th order values from high end

=28.4 + 32.6

2= 30.5




17/27


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



=11.2 + 13.5

2

= 12.35

Q3 = average of 3rd & 4th order values from high end

=28.4 + 32.6

2= 30.5




18/27

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





19/27


n = 2139.60 40.52 40.56 42.65 44.40 44.62 45.95 48.56 49.93 50.37

51.68


20/27


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


Q1 = average of 5th & 6th order values from low end

=44.40 + 44.62

2= 44.51




21/27


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



=44.40 + 44.62

2= 44.51

Q3 = average of 5th & 6th order values from high end

=55.00 + 56.02

2= 55.51




22/27


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



=44.40 + 44.62

2= 44.51

Q3 = average of 5th & 6th order values from high end

=55.00 + 56.02

2= 55.51




23/27

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




24/27


n = 15

550 560 575 600 625 625 650

675


25/27


n = 15

550 560 575 600 625 625 650

675

700 725 740 750 775 850 1100


2 = 4

Q1 = 4th order value from low end = 600




26/27


n = 15

550 560 575 600 625 625 650

675

700 725 740 750 775 850 1100


2 = 4


Q3 = 4th order value from high end = 750




27/27


n = 15

550 560 575 600 625 625 650

675

700 725 740 750 775 850 1100


2 = 4


Q3 = 4th order value from high end = 750


fivenumsummti.pdf

Documents