STA301 Assignment No. 1 solution
Friday, October 29, 2010 Posted In STA Edit ThisAssignment No.1 (Course STA301)
Fall 2010 (Total Marks 30)
Deadline
Your Assignment must be uploaded/ submitted before or on
23:59 29th 4th Nov, 2010
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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.
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.
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,
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
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
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.
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
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
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
