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Statistics assignment Sample Questions and Answers:
Question 1 : Define Rank Correlation and derive p (X. Y).
Ans. Let us suppose that a group of n individuals is arranged in order of merit or proficiency in
possession of two characteristics A and B. These ranks in the two characteristics will, in general,
be different B. These ranks in the two characteristics will, in general. be different For example, if
we consider the relation between intelligence and beauty. it is not necessary that a beautiful
individual is intelligent also. Let (x, y) : I = 1, 2…. n be the rank of the ith individual in two
characteristics A and B respectively. Pearsonian coefficient of correlation between the ranks x’, s
and 𝑦𝑖’ is called the rank correlation coefficient between A and B for that group of individuals.
Derivation of p(X, Y) : We have
P(X,Y) =
x− x Y− Y
[ (x− x)2. (Y− Y)2 =
𝑥𝑦
𝑥2. 𝑦2
…(1)
Where x = X - 𝑥 . y = Y - 𝑌.
If X and Y each takes the values 1,2,….. n then 𝑥 =
𝑛+1
2
= 𝑌
and n𝜎
2
𝑥
= 𝑥2
=
𝑛 (𝑛2−1)
12
and n𝜎
2
𝑦
= 𝑦2
=
𝑛(𝑛2−1)
12
…(2)
Also 𝑑2
= (𝑥 − 𝑦)2
= (𝑥 − 𝑥) – (Y - 𝑌)]2 = 𝑥 − 𝑦 2
= 𝑑2
= 𝑥2
+ 𝑦2
- 2 𝑥𝑦
= 𝑥𝑦 =
1
2
( 𝑥2
+ 𝑦2
- 𝑑
2
)

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We shall now investigate the effect of common ranking (in case of ties). on the sum of squares of
the ranks. Let 𝑆2
and S1
2
denote that sum of the squares of united and lied ranks respectively.
Then we have:
Question 2 : Report the data given in the illustration 13 by a frequency polygon drawn
straightway.
Solution Frequency Polygon
(Showing the wage distribution of a group of workers)

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Question 3 : The equation for yearly sales (in ’000 $.) for a commodity with the year, 2003 as
origin is
Yc =91.6 + 28.8X. Determine the trend equation to give the monthly trend values with Jan ’04.
Since, the conversion is required to be made from a higher periodical base (annual) to a lower
periodical base (monthly), it is necessary to attempt on the conversion first, and then on shifting
of the trend origin as follows :
(ii) Conversion of the trend
By the formula of conversion of an annual trend into a monthly one we have,
Yc =
𝑎
12
+
𝑏𝑋
12 ×12
Substituting the respective values, in the above we get,
Yc =
91 .6
12
+
28.8𝑋
12 ×12
= 7.63 + 0.2X
Thus, Yc = 7.63 + 0.2 Y
When X unit = 1 month, and Y unit = monthly sales
(ii) Shifting of the Trend Origin
Here, it is required to shift forward the trend origin by 6.5 months i.e. from 1st July, 03 (the
midpoint of the year, 03) to the 15th Jan, 04 (the midpoint of the month).
Thus, K = 5.5

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By the formula of shifting a trend we have,
Yc = a + b (X + K)
Substitution the respective values in the above we get,
Yc = 7.63 + 0.2 (X + 6.5)
= 7.63 + 0.2X + 1.3
= 8.93 + 0.2 Y
Yc = 8.93 + 0.2 X
Where, the point of origin is Jan ’03, X unit = 1 month, and Y unit monthly sales.
(iii) Calculation of the trend value for March ’04
The time deviation of March ’04 from the trend origin Jan ’04, or X = 2
Thus, when X = 2, Yc = 8.93 + 0.2 (2)
= 8.93 + 0.4 = 9.33
Hence, the trend value for March ’04 will be 9.33.