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About Statistics:
Statistics is a subject that deals with
collection, tabulation, presentation,
analysis and interpretation of the
numerical data. Statistics assignment
are generally used in our day-to-day
life to make decisions that may be
related to our own business or job,
personal work, and/or for some other
reasons, where these decisions are mostly
taking under the conditions of
uncertainty. For example, a businessman,
who is having sufficient experience in his
own business, can estimate the sales of a
particular product on the forthcoming week based on the sales of the same product during
the previous months. In this example, the businessman using statistics for estimating the
sales of a product only based on his experience, but not based on any standard statistical
models. Similarly, the usage of statistics is widely increased in each and every field that
deals with qualitative or quantitative data or both. In particular, due to a phenomenal
growth in science and technology, the application of statistical theory and its methods are
highly increasing in various disciplines such as Actuarial Science, Biostatistics, Business
Analytics, Econometrics, Epidemiology, Reliability Engineering, and Statistical Finance.

Statistics Homework Sample Questions & Answers
Illustration: 1
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
𝑋1
𝑋2
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.

(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
𝑋𝑐 =
𝑋2− 𝑋1
𝑁
=
30−20
3
= 3.33
Let the average of origin be 𝑋1 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
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.
Illustration 2.
(On odd number of data)
Fit a trend line to the following series by the method of semi averages. Also, determine the
trends values both by location and by computation of the average change.
Day :
Sales in
$:
Sun
125
Mon
130
Tue
135
Wed
110
Thu
105
Fri
110
Sat
115

Solution: Computation of the Semi Averages
Days Sales in $. Semi totals Semi averages Semi averages
points
Sun
Mon
Tue
Wed
Thu
Fri
Sat
125
130
135
110
105
110
115
390
330
130
110
𝑋1
𝑋2
With the above semi averages of 130 for Monday, and 110 for Friday, the trend line is fitted
to the given date as under:
Graphic Representation of the Trend Line by the method of Semi Average

(b) Computation of the Trend values
(i) By location on the trend line
Days :
Trend
value
S
135
M
130
T
125
W
120
TH
115
F
110
SA
105
(ii) By the average change
The average change 𝑋𝑐 =
𝑋2−𝑋1
𝑁
=
110−130
𝑁
= -5
Here, N = 4 days, because there is a gap of 4 days between Friday and Monday
representing 𝑋2 and 𝑋1 respectively. Taking the average of origin to be 𝑋2 i.e., 110. The
trend values are computed as under:

Days Time dvn. From the
average of origin i.e.
Friday
Trend values
Y = 𝑿 𝟐 +
𝑿 𝟐− 𝑿 𝟏
𝑵
.x
Sun
Mon
Tue
Wed
Thu
Fri
Sat
-5
-4
-3
-2
-1
0
1
110 + ( -5 × -5 ) = 135
110 + ( -5 × -4) = 130
110 + ( -5 × -3) =125
110 + (-5 × -2) =120
110 + (-5 × -1 ) = 115
110 + (-5 × -10 ) = 110
110 + (- 5 × 1) = 105
(iv) Moving Average Method
Under this method, the trend line is fitted to a series on the basis of its moving averages
which represent the trend value of the series. The technique of calculating the moving
averages have been discussed at length in the chapter entitled “Measures of different
groups of a set of figures are computed in a moving manner. Each group ends with the last
item, and at each advancing step the group is included in the next group is left aside, and
the first group begins with the first item, and the last group ends with the last item, and at
each advancing step the first item of the preceding group ends with the last item, and at
each advancing step the first item of the preceding group is left aside, and one more item
that succeeds the group is included in the next group to get the moving averages thereof.
Each group may consist of 2,3,4,5,6,7,9 or 12 numbers of items depending on the size of
the series and purpose of the study. Symbolically these may be computed as follows :
In case of 3 tons:
MA1 =
𝑋1+ 𝑋2+ 𝑋3
3
, 𝑀𝐴2 =
𝑋2+ 𝑋3+ 𝑋4
3
MA3 =
𝑋3+ 𝑋4+ 𝑋5
3
and so on
In case of 5 tons: M.A1 =
(𝑋1+ 𝑋2 𝑋3+ 𝑋4+ 𝑋5)
5
,
MA2 =
(𝑋2+ 𝑋3+𝑋4+ 𝑋5+ 𝑋6)
5
, and son on
The total, and the average figure of each group are placed against the middle item of the
group in the adjacent column respectively. If the number of items in the groups is even,
then the total and average of groups are placed, in the first instance, just against the
middle points of the respective groups, and then the averages of the adjacent averages are
placed against the mid item of the respective groups. This process of averaging the

averages is called centering, which is very much done in case of even numberly moving
averages.
It may be noted that the greater the number of items taken in the groups for averaging, the
greater will be the blank of moving averages for the extreme items of a series. For example,
in case of 9 yearly moving averages, we will not have any average figures for the first 4,
and last 4 items of the series. This is because, in such cases, the averages figures are
placed only against the middle item i.e. the 5th item leaving aside the 4 items before, and 4
items after in all the groups. Hence, unless the series is abnormally a lengthy one, it is
advisable to find the moving averages of smaller groups consisting of 3, or 5 items only so
that we may cover the entire series by the moving averages leaving aside only one, or two
items at each of the extremes. Further, for these few blank spaces we can estimate the
average values with greater degree of accuracy with reference to the nature of increase, or
decrease in the adjacent average figures.

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