STA301 Assignment No. 1 solution

Assignment No.1 (Course STA301)

 Spring 2011 (Total Marks 30)

Deadline

Your Assignment must be uploaded/ submitted before or on 21^stApril, 2011

STUDENTS ARE STRICTLY DIRECTED TO SUBMIT THEIR ASSIGNMENT BEFORE OR BY DUE DATE. NO ASSIGNMNENT AFTER DUE DATE WILL BE ACCEPTED VIA E.MAIL).

Rules for Marking

It should be clear that your Assignment will not get any credit IF:

• The Assignment submitted, via email, after due date.
• The submitted Assignment is not found as MS Word document file.
• There will be unnecessary, extra or irrelevant material.
• The Statistical notations/symbols are not well-written i.e., without using MathType software.
• The Assignment will be copied from handouts, internet or from any other student’s file. Copied material (from handouts, any book or by any website) will be awarded ZERO MARKS. It is PLAGIARISM and an Academic Crime.
• The medium of the course is English. Assignment in Urdu or Roman languages will not be accepted.
• Assignment means Comprehensive yet precise accurate details about the given topic quoting different sources (books/articles/websites etc.). Do not rely only on handouts. You can take data/information from different authentic sources (like books, magazines, website etc) BUT express/organize all the collected material in YOUR OWN WORDS. Only then you will get good marks.

Objective(s) of this Assignment:

• The assignment is being uploaded to strengthen the students’ BASIC concepts about statistics.
• Hands on arranging and displaying already collected data into an organized form, using given statistical method.
• Make students able to understand the concept of measures of central tendency and measures of dispersion. 

Assignment.1 (Lessons 1-11)

Question 1:                                                                                Marks: 4+3+3=10

a) Answer the following questions.

      i.        What are the main goal /Purpose of Statistical Inference?

     ii.        Write down names of methods of allocation the sample size in stratified sampling.

b). Find the missing frequencies and complete table.                         

x	f	c.f	Relative .f
2			3/25
4	2
6		8
8	4
total		25	1

c) From the following data, represent the different subjects in two classes and no. of students on various subjects of a college by making multiple bar charts.

Subjects	English	Mathematics	Statistics	Pak. Studies	Urdu
Class A	40	33	21	80	19
Class B	50	39	30	68	10

Question 2:                                                                                Marks: 4+3+3=10

a) Answer the following questions

i.             Define a bi-model distribution.

ii.            The relation between A.M , G.M and H.M is

Under what situation these are equal.

b). By using an appropriate average find out the average rate of motion in the case of a person who rides the first mile at the rate of 10 miles per hour the next mile at the rate of 8 miles per hour and the third at the rate of 6 miles per hour.

c) Find out average (percent) increase in population, if the population in the first decade has increased 20%, in next decade 25% and in the third decade 4 %.

Question 3:                                                                                Marks: 3+4+4=10

a) How many observations (n) are involved in computing the mean deviation (M.D) if: M.D=2.67, Σd= 16

b) Find the value of “h” by using the following data             

l= 19.5, h=? f=41, n/4=50, cf= 39, Q1=24.865

c) Find the coefficient of variation (CV) for the data given below,

Working hours per month (Y):       111, 123, 153, 173, 129

SOLUTION: Thanks to Imran Ilyas to share this solution

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Question No. 2

Define a bi-model distribution.

A bimodal distribution most commonly arises as a mixture of two different unimodal distributions (i.e. distributions having only one mode). In other words, the bimodally distributed random variable X is defined as Y with probability α or Z with probability (1 − α), where Y and Z are unimodal random variables and 0 < α < 1 is a mixture coefficient.

ii. The relation between A.M , G.M and H.M is

A.M ³G.M ³ H.M

Under what situation these are equal.

Answer:

If data is symmetric then these are equal to each other.

b). By using an appropriate average find out the average rate of motion in the case of a person who rides the first mile at the rate of 10 miles per hour the next mile at the rate of 8 miles per hour and the third at the rate of 6 miles per hour.

c) Find out average (percent) increase in population, if the population in the first decade has increased 20%, in next decade 25% and in the third decade 4 %.

Question 3:

a) How many observations (n) are involved in computing the mean deviation (M.D) if: M.D=2.67, Σd= 16

MD=Σd/n=

n=Σd ×MD16/2.67=5.99 approximately

But n is a number of observation so n = 6

b) Find the value of “h” by using the following data

l= 19.5, h=? f=41, n/4=50, cf= 39, Q1=24.865

Q1 = l+h/f(n/4-c)

Putting the value of these and then solving.

H = 20

c) Find the coefficient of variation (CV) for the data given below,

Working hours per month (Y): 111, 123, 153, 173, 129

Using this data we have S = 49.85 and X = 137.8

CV= 49.85/137.8 ×100%

= 36.18%