### STA 301 Statistics and Probability Assignment No.1 Fall Spring 2013 Due Date: December 02, 2013

STA 301 Assignment No.1 (Non-Graded) Fall 2013 (Total Marks 20)

Deadline

Your Assignment must be uploaded/ submitted before or on 23:59 December 02, 2013

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

Instructions:

This assignment is NON-GRADED, So has NO weightage in the final grade. Assignment is given for your learning and practice purpose only.

The submitted Assignment should found as MS Word document file.

The Statistical notations/symbols should well-written i.e., using MathType software.

The Assignment should not 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 build up the students concepts regarding frequency distribution and manipulation of data.

This assignment will strengthen the basic idea about the concept of measure of central tendency and measure of dispersion.

Assignment No: 1 (Lessons 1-11)

Question 1: Marks: 6

Make the frequency distribution table by using the class interval of 15 and the total number of classes as 6. Clearly construct the columns of class limits, frequency and class boundaries. The data is given below:

62, 73, 85, 42, 68, 54, 38, 27, 32, 63, 68, 69, 75, 59, 52, 58, 36, 85, 97, 72, 52, 52, 63, 68, 29, 73, 29, 76, 29, 57, 46, 43, 28, 32, 09, 66, 72, 68, 42, 76.

Answer:

A frequency table with intervals is a table that has the number of data values falling in a range that is specified by an interval. It is constructed by first determining the data range of data set, then deciding the particular width of the class intervals and lastly, dividing the range with the selected width of the class interval to know the number of intervals.

Class limits

Frequency

Class Boundaries

09—23 1 8.5 —23.5

24—38 9 23.5—38.5

39—53 7 38.5—53.5

54—68 12 53.5—68.5

69—83 8 68.5—83.5

84—98 3 83.5—98.5

Question 2: Marks: 3+5=8

a) Calculate the arithmetic mean for the following data

Classes

(Mileage Rating)

Frequency

20.0 – 22.9

2

23.0 – 25.9

4

26.0 – 28.9

14

29.0 – 31.9

8

32.0 – 34.9

2

Total

30

Answer:

Arithmetic Mean Definition:

Arithmetic mean is commonly called as average.Mean or Average is defined as the sum of all the given elements divided by the total number of elements.

Formula:

Mean = sum of elements / number of elements

= a1+a2+a3+…..+an/n

Example: To find the mean of 3,5,7.

Step 1: Find the sum of the numbers.

3+5+7 = 15

Step 2: Calculate the total number.

there are 3 numbers.

Step 3: Finding mean.

15/3 = 5

b) Find the median from the following data.

Class

Frequency

0 up to 5

2

5 up to 10

7

10 up to 15

12

15 up to 20

6

20 up to 25

3

25 up to 30

1

30 up to 35

2

35 up to 40

3

Total

36

Question 3: Marks: 6

Find the coefficient of variation (C.V) for the following prices of a commodity.

Price (X): 8, 13, 18, 23, 30, 40, 45, 52, 56, 58, 63, 64, 68, 70, 76, 83, 86, 92

Answer:

Coefficient of Variation Example

Coefficient of Variation is the percentage variation in mean, standard deviation being considered as the total variation in the mean. If we wish to compare the variability of two or more series, we can use the coefficient of variation. The series of data for which the coefficient of variation is large indicates that the group is more variable and it is less stable or less uniform. This below worksheet illustrates how to calculate coefficient of variation for the given data set. The coefficient of variance is a dimensionless number.

Formula for Coefficient of Variance

Coefficient of Variation Cv = Standard Deviation / Mean

In other words coefficient of variation is defined ratio of the Standard Deviation to the Mean. The value of CV is calculated only for non-zero mean. You can know more about Standard deviation from this Standard Deviation Worksheet

Example to Find Coefficient of Variance

1. Find CV of {13, 35, 56, 35, 77}

Solution:

Number of terms (N) = 5

Mean:

Xbar = (13 + 35 + 56 + 35 + 77)/5

= 216/5 = 43.2

Standard Deviation (SD):

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