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Objective(s) of this Assignment:

 

The assignment is being uploaded to build up the students concepts regarding:

 

  1. 1.   Measurement scale
  2. 2.   Stem and leaf
  3. 3.   Manipulation of data
  4. 4.   Measures of Central tendency

 

 

 

 

 

 

 

 

 

Assignment No: 1 (Lessons 1-9)

   Question 1:                                                                                                              Marks: 4+3=7

 

  1. Given the following frequency distribution:

     

Class Limits

Frequency

118 – 126

3

127 – 135

5

136 – 144

9

145 – 153

12

154 – 162

5

 

     Construct the columns of Class Boundaries, Relative Frequency, Mid points and

      Cumulative frequency.

  1. The ages of 22 patients admitted to a certain hospital during a particular week were as

follows:

66, 73, 68, 54, 25, 38, 67, 69, 74, 53, 52, 72, 55, 75, 37, 24, 13, 12, 11, 26, 39, 23

Construct a Stem and Leaf display for the above data. 

 

  Question 2:                                                                                                              Marks: 6+2=8

 

  1. Ten students (graduates and undergraduates) are enrolled in the course on statistics. Their weights are given below:

52, 63, 73, 58, 88, 72, 60, 76, 69, 74

Calculate Arithmetic mean, Geometric mean and Harmonic mean for the above data.

    b.    Which scale of measurement is more suitable in the following examples?

  • Religion can be categorized as Jewish, Muslim, Christian, Buddhist and “Other”.
  • A teacher ranks the students according to their oral language skills.
  • The number of minutes of overtime work that employees perform.
  • The number of questions asked by a customer during a simulated encounter with a salesperson.

  

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Replies to This Discussion

A.Mean=68.5

G.Mean=67.6

H.Mean=67.11

plz correct me if i am wrong

A.M = 68.5

G.M = 67.7

H.M = 67.2

 

    b.    Which scale of measurement is more suitable in the following examples?

  • Religion can be categorized as Jewish, Muslim, Christian, Buddhist and “Other”.

Ans: Nominal scale of measurement

  • A teacher ranks the students according to their oral language skills.

Ans:Ordinal or ranking scale

  • The number of minutes of overtime work that employees perform.

Ans:ratio scale

  • The number of questions asked by a customer during a simulated encounter with a salesperson.i have no idea about this one

which measurement scale is used for fourth statement?

option c is correct

measurement of scale is used for 3rd statement

Geometric Mean Definition:
Geometric mean is a kind of average of a set of numbers that is different from the arithmetic average. The geometric mean is well defined only for sets of positive real numbers. This is calculated by multiplying all the numbers (call the number of numbers n), and taking the nth root of the total. A common example of where the geometric mean is the correct choice is when averaging growth rates.


Geometric Mean Example: To find the Geometric Mean of 1,2,3,4,5.

Step 1: N = 5, the total number of values. Find 1/N.
1/N = 0.2 

Step 2:Now find Geometric Mean using the formula.
((1)(2)(3)(4)(5))0.2 = (120)0.2 
So, Geometric Mean = 2.60517

This example will guide you to calculate the geometric mean manually.

Harmonic Mean Definition:
Harmonic mean is used to calculate the average of a set of numbers. Here the number of elements will be averaged and divided by the sum of the reciprocals of the elements. The Harmonic mean is always the lowest mean.

Harmonic Mean Formula :
Harmonic Mean = N/(1/a1+1/a2+1/a3+1/a4+.......+1/aN)
where 
X = Individual score 
N = Sample size (Number of scores)



Harmonic Mean Example: To find the Harmonic Mean of 1,2,3,4,5.

Step 1: Calculate the total number of values.
N = 5 

Step 2: Now find Harmonic Mean using the above formula.
N/(1/a1+1/a2+1/a3+1/a4+.......+1/aN)
= 5/(1/1+1/2+1/3+1/4+1/5)
= 5/(1+0.5+0.33+0.25+0.2)
= 5/2.28
So, Harmonic Mean = 2.19

This example will guide you to calculate the harmonic mean manually.

Arithmetic Median Definition:
Median is the middle value of the given numbers or distribution in their ascending order.Median is the average value of the two middle elements when the size of the distribution is even.

Example 1: To find the median of 4,5,7,2,1 [ODD].
Step 1: Count the total numbers given.
There are 5 elements or numbers in the distribution.

Step 2: Arrange the numbers in ascending order.
1,2,4,5,7

Step 3: The total elements in the distribution (5) is odd.
The middle position can be calculated using the formula. (n+1)/2 
So the middle position is (5+1)/2 = 6/2 = 3 
The number at 3rd position is = Median = 4

Example 2: To find the median of 4,5,7,2,1,8 [Even]
Step 1: Count the total numbers given.
There are 6 elements or numbers in the distribution.

Step 2: Arrange the numbers in ascending order.
1,2,4,5,7,8

Step 3: The total elements in the distribution (6) is even.
As the total is even, we have to take average of number at n/2 and (n/2)+1
So the position are n/2= 6/2 = 3 and 4 
The number at 3rd and 4th position are 4,5

Step 4: Find the median.
The average is (4+5)/2 = Median = 4.5


hope u will understand if any confusion dn ask...

Thank u so much bro

Thnks Sir Tariq Malik.

thanks

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