s1 measures of dispersion.ppt

8/14/2019 S1 Measures of Dispersion.ppt

1/14

S1 Averages and Measures

of Dispersion


2/14

S1 Measures of Dispersion

Objectives:To be able to find the median and

quartiles for discrete data

To be able to find the median and

quartiles for continuous datausing interpolation


3/14

Can you work out the rule for finding median

and quartiles from discrete data?

LQ Median UQ

1 2 3 4 5 1.5 3 4.5

1 2 3 4 5 6

1 2 3 4 5 6 7

1 2 3 4 5 6 7 8

1 2 3 4 5 6 7 8 9 Can you spot any rules for n amount of

numbers in a list?


4/14

LQ n/4

If n/4 is a whole number find the mid point

of corresponding term and the term above

If n is not a whole number, round the

number up and find the corresponding

term

UQ 3n/4

If 3n/4 is a whole number find the mid

point of corresponding term and the term

aboveIf n is not a whole number, round the

number up and find the corresponding

term


5/14

Mediann/2

If n/2 is a whole number find the midpoint

of the corresponding term and the term

above

If n/2 is not a whole number, round up and

find the corresponding term


6/14

Calculate the mean, median and inter quartile

range from a table of discrete data

Number of

CDs(x)

Number of

students (f)

35 3

36 17

37 29

38 34

39 12

Mean = fx

f


7/14


range from a table of discrete dataNumber of

CDs(x)

Number of

students (f)

35 3

36 17

37 29

38 34

39 12

Cumulative

frequency

3

20

49

83

95

Median = n/2

Median = 95/2 =

47.5 = 48thvalue

Median = 37 CDs

LQ = 95/4 = 23.75

LQ = 24thvalue

LQ (Q1) = 37 CDs

UQ (Q3) = 95/4 x 3

= 71.25UQ = 72ndvalue

UQ (Q3) = 38 CDsIQR = Q3-Q1 = 38-37=1


8/14


range from a table of continuous dataLength of

flower stem(mm)

Number of

flowers (f)

30-31 2

32-33 2534-36 30

37-39 13

Cumulative

frequency

2

2757

70

Median = n/2

We do not need to

do any rounding

because we are

dealing with

continuous data

Median = 70/2 =

35thvalue

This lies in the 34-36 class but we

dont know the

exact value of the

term


9/14

Using interpolation to find an estimate for the

median

33.5mm 36.5mm

27 5735

m

m33.5 = 35 - 27

36.533.5 = 57 - 27

m 33.5 = 83 30

m33.5 = 0.26 x 3

m = 33.5 + 0.8 = 34.3


10/14


lower quartile

31.5mm 33.5mm

2 2717.5

Q1

Q131.5 = 17.5 - 2

33.531.5 = 27 - 2

Q1 31.5 = 15.52 25

Q131.5 = 0.62 x 2

Q1 = 31.5 + 1.24 = 32.74

LQ = 70/4 = 17.5 (in the 32-33 group)


11/14


upper quartile

33.5mm 36.5mm

27 5752.5

Q3

Q333.5 = 52.5 - 27

36.533.5 = 57 - 27

Q3 33.5 = 25.53 30

Q333.5 = 0.85 x 3

Q1 = 33.5 + 2.55 = 36.05

UQ = 70/4x3 = 52.5 (in the 34-36 group)


12/14

Summary of rulesn = total frequency

w = class width

fB = cumulative frequency below median/lq/uqfU = cumulative frequency above median/lq/uq

Median = LB + n fB x w

fU - fB

LQ = LB + n fB x w

fU - fB

UQ = LB + n

fB x w

fU - fB


13/14

The lengths of a batch of 2000 rods were measured to the nearest

cm. The measurements are summarised below.

Length

(nearest cm)

Number of

rods

60-64 11

65-69 49

70-74 190

75-79 488

80-84 632

85-89 470

90-94 137

95-99 23

Cumulative

frequency

11

60

250

738

1370

1840

19772000

Q1=74.5 + 500-250 x 5

738-250Q1=77.06

Q2=79.5+1000-738 x 5

1370-738Q2=81.57

Q3=84.5+1500-1370 x 5

1840-1370Q3=85.88

By altering the formula slightly can you work out how to find the 3rd

decile (D3) and the 67th

percentile (P67)?


14/14

Answers

D3=74.5 + 600-250 x 5738-250

D3=78.09

P67=79.5 + 1340-738 x 5

1370-738

P67=84.26

s1 measures of dispersion.ppt

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