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Sample Statistics Homework Help Illustration and Solutions:

Represent the following data by a suitable graph:

Illustration: 1

Month:

Sales

in ’000

$ :

Jan.

5

Feb

7

March

10

April

15

May

18

June

20

July

19

Aug.

17

Sept.

25

Oct.

27

Nov.

34

Dec.

26

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Solution:

Graphic Representation of data relating to sales during a year

2. Graphs with double scale

A graph on natural scale may be drawn either with a single scale shown as above or with

double scales. When two variables represented by Y. axis are in two different units, say,

Rs. And Tonnes, then it is required to draw the graphs with different scales-one fixed on

the left hand side and the other on the right or left hand side. In such a case, the

average values of both the variables are kept in the middle of the graphs, and two scales

are marked in proportion to their respective average values. This sort of scalling

facilitates comparison between the two variables.

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Illustration 2. (On even Number of Data)

From the following data. Fit a trend line, and determine the trend values by the method

of semi average. Also, forecast the trend value for the year 2002.

Year Output (in’ 000 units)

1999 20

200 16

2001 24

2002 30

2003 28

2004 32

Solution:

(a) Computation of Semi Averages.

Year Outputs Semi totals Semi averages Semi average points

1999

2000 2001 2002 2003 2004

20

16 24 30 28 32

60 90

20 30

𝑋 1

𝑋 2

With the above semi averages of 20 for 2000 and 30 for 2003 the trend line is fitted to

the given series as under:

Graphic Representation of the Trend Line by method of Semi averages.

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(b) Computation of trend values by location on the trend line

Years :

Outputs

(in ’000

units)

1999

15.67

2000

20

2001

23.33

2002

26.67

2003

30

2004

33.33

2005

36.67

Alternative

Computation of the trend values by the averages change

The average change is given by

𝑋 𝑐 = 𝑋 2− 𝑋 1

𝑁

= 30−20

3 = 3.33

Let the average of origin be 𝑋 1 i.e. 20.

Thus the trend values will be computed as under:

Year Time dvn.from the time

of origin

= 2000

Trend Values

T = 𝑿 𝟏 + 𝑿 𝟐− 𝑿 𝟏

𝑵 . x

(T)

1999

200

2001

2002

2003

2004

2005

-1

0

1

2

3

4

5

20 + 3.33(-1) – 16.67

20 + 3.33 (0) = 20.00

20 + 3.33 (1) = 23.33

20 + 3.33 (2) = 26.67

20 + 3.33 (3) = 30.00

20 + 3.33 (4) = 33.33

20 + 3.33 (5) = 36.67

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From the above, it must be noticed that the required trend value for 2002 is 26.67.

Further, it must be seen that the trend values computed as above are the same as those

located from the trend line shown above.