STA301 Assignment No. 1 solution

Assignment No.1 (Course STA301)

 Fall 2010 (Total Marks 30)

Deadline

Your Assignment must be uploaded/ submitted before or on

23:59 29^th 4^th Nov, 2010   

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.
•  How to recognize and differentiate among different types of data in real life examples.
• 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: 5+5=10

Give an answer of the followings:

• Define an array.
• University students have been assigned roll no’s according to their marks. Which scale of measurement is used to assign the roll numbers?
• When statistical results are misleading?

(b) Make discrete frequency distribution from the given data,

       1,2,3,2,1,2,1,3, 4,5,1,2,3,1,4,2, 2,3,2,1,4,4,4,2,1,    

Also find;

• Cumulative frequencies
• Relative frequencies

Question 2:                                                                                                                        Marks: 2+8=10

(a) Find Geometric mean from the following data.

1, 2, 3,2,4,5,4,3,4,-1,4, 3,0,1,-3, 2,4

(b) The weight of the 40 male students at a university is given in the following frequency table:

Weight	frequency
118-126	3
127-135	5
136-144	9
145-153	12
154-162	5
163-171	4
172-180	2

Calculate median and mode from the above data.

Question 3:                                                                                                                      Marks: 2+2+6 =10

(a) Why Quartile deviation is better than the Rang?

(b) For given data calculate range and coefficient of range,

0.035, 0.045, 0.031, 0.044, 0.032

(c) Calculate an appropriate measure of dispersion for the following data.

Farm Size (acre)	No. of Farms
Bellow 40	394
41-80	461
81-120	391
121-160	334
161-200	169
201-240	113
241 and above	148

                                                             


Solution:

Q.NO.1

ARRAY

1. to place in proper or desired order; marshal: Napoleon arrayed his troops for battle.

2. to clothe with garments, esp. of an ornamental kind; dress up; deck out: She arrayed herself in furs and diamonds.

3. order or arrangement, as of troops drawn up for battle.

4. military force, esp. a body of troops.

5. a large and impressive grouping or organization of things: He couldn't dismiss the array of facts.

6. regular order or arrangement; series: an array of figures.

7. a large group, number, or quantity of people or things: an impressive array of scholars; an imposing array of books.

8. attire; dress: in fine array.

9. an arrangement of interrelated objects or items of equipment for accomplishing a particular task: thousands of solar cells in one vast array.

10. Mathematics, Statistics .
a. an arrangement of a series of terms according to value, as from largest to smallest.
b. an arrangement of a series of terms in some geometric pattern, as in a matrix.

11. Computers . a block of related data elements, each of which is usually identified by one or more subscripts

Q1(b)

Make discrete frequency distribution from the given data,
1,2,3,2,1,2,1,3, 4,5,1,2,3,1,4,2, 2,3,2,1,4,4,4,2,1,

X                           F                           CF                         rf

1                           7                           7                           7/25=0.28

2                           8                           15                          8/25=

3                           4                           19                          4/25=

4                           5                           24                          5/25=

5                           1                           25                          1/25=

  

Question 2: (a) Find Geometric mean from the following data.
1, 2, 3,2,4,5,4,3,4,-1,4, 3,0,1,-3, 2,4


AS WE can see data contain 0 we can not take log for 0 so it is impossible to solve this question for Geometric mean

Remember when data have 0 we cannot compute Geometric mean as well as harmonic mean

For given data calculate range and coefficient of range,
0.035, 0.045, 0.031, 0.044, 0.032

Range=0.045-0.031=0.014

coefficient of range=0.045-0.031/0.045+0.031
=0.014/0.076
=0.1842

QNO3(A):
The quartile deviation is superior to range as it is not affected by extremely large or small observations. It is simple to understand and easy to calculate. The quartile deviation is as widely used as other measures of dispersion. It is used in situations where extreme observations are thought to be unrepresentative.

When statistical results are misleading?

The world is littered with statistics, and the average person is bombarded with five statistics a day1. Statistics can be misleading and sometimes deliberately distorting. There are three kinds of commonly recognised untruths:

Lies, damn lies and statistics.
- Mark Twain
This quote from Mark Twain is accurate; statistics are often used to lie to the public because most people do not understand how statistics work. The aim of this entry is to acquaint the reader with the basics of statistical analysis and to help them determine when someone is trying to pull a fast one.

Think about how stupid the average person is; now realise half of them are dumber than that.
- George Carlin
There are many books which teach statistics, but they are mostly big and heavy mathematical books, which cost a lot of money, and which may require a degree in the subject to understand anyway. For many years there has been a need for a Statistics for Dummies book and in fact there is one, written by Deborah Rumsey. On the Internet information on how to understand statistics can be found, but the sites mostly cater for medical students who need to examine experimental drug studies, although a great online starting place is RobertNiles.com, which explains how to examine statistics for errors and how to create your own statistics correctly

  

(c) Calculate an appropriate measure of dispersion for the following data.
In this situation we will calculate Quartile deviation be cause we can not find value for X due to open end classes so we will be unable to compute S.D variance mean deviation average etc only quartile deviation is suitable calulate it your self