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Assignment No: 1 (Lessons 1-9)
Question 1: Marks: 4+3=7
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.
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
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?
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+ Click Here to Search (Looking For something at vustudents.ning.com?) + Click Here To Join (Our facebook study Group)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?
Ans: Nominal scale of measurement
Ans:Ordinal or ranking scale
Ans:ratio scale
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/a_{1}+1/a_{2}+1/a_{3}+1/a_{4}+.......+1/a_{N})
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/a_{1}+1/a_{2}+1/a_{3}+1/a_{4}+.......+1/a_{N})
= 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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