# Statistics External Correspondence Previous Year Question Paper Year 2006 : IIIrd Year Part II

** Q. l.** (a) Name the components of time series.

(b) Do you agree that r limits are between 1 to – 1 ?

(c) Show graphically the position of Mean, Median and Mode in a positively and negatively skewed curves.

(d) Why S.D. (Standard Deviation) is considered a better method of variation as compared to M.D. (Mean Deviation)?

(e) Is statistics a science or an art or both?

**Answer : **

**Q. 2.** (a) A distribution consists of three components with total frequencies of 200,250 and 300 having means 25,10 and 15 respectively. Find the mean of combined distribution.

(b) In a series with 100 items, having simply mean of 40, later on it was discovered that two items of 45, 35 were wrongly taken as 35 and 25. Find the correct mean.

(c) A man travelled by auto for 3 days. He covered 480 kilometres each day. He drove the first day 10 hours @ 48 kilomeÂ¬tres per hour, the second day 12 hours @ 40 kilometres per hour and the third day 15 hours fa) 32 kilometres per hour. What was his average speed ?

**Answer : **

**Q. 3. **(a) Compute coefficient of Q.D. and skewness from these values:

Q1 = 14.6

Median = 18.8

Q3 = 25.2

(b) The following is the record of goals scored by team A in a football season:

**No. of Goals scored **: 0-1-2-3-4

**No. of Matches** : 1-9-7-5-3

For team B, the average number of goals scored per match was 2.5 with a standard deviation of 1.25 goals.

Find which team may be considered more consistent.

(c) List the various methods of measuring dispersion. CalÂ¬culate the value of S.D. (Standard Deviation), if X =45, Mode = 48 and coefficient of skew ness = – 0.4.

**Answer : **

**Q. 4.** (a) Define Index Number. Explain the problems while constructing the index number.

(b) Compute:”

(i) Laspeyre’s;

(ii) Paasche’s;

(iii) Fisher;

(iv) Bowley’s, index numbers from the following tabie:

**Items- P0 – q0 – p1 – q1**

A – 10 – 4 – 12 – 6

B – 15 – 6 – 20 – 4

C – 2 – 5 – 5 – 3

D- 4 – 4 – 4 – 4________

(c) The correlation (r) coefficient between two variables is found to be 0.75 of 100 items. Comment upon the value of correlation.

**Answer : **

**Q.5** (a) How many models are used while analyzing the time series State algebraically.

(b) Fit a straight line trend by method of least squares and estimate the for 2006:

**Year** – 2000 – 2001 – 2002 – 2004 – 2005

** Sales ** – 12 – 13 – 14 – 15 – 26

(c) From the fallowing data , compute coefficient of correlation (r) between X and Y:

**A aeries-Y aeries**

**– X ** – 25 – 18

**SquareofDeviationsfromA.M. ** – 136 -, 138

**Summation of products of
deviations of X and Y series from
their respective means ** – 122

**Number of pairs of values ** – 15

**Answer : **