Question 1 :
Calculate the standard deviation of the following data.
38, 40, 34, 31, 28, 26, 34
Solution :
First write the given data in the ascending order.
26, 28, 31, 34, 34, 38, 40
x̄ = Σx/n
= (26+28+31+34+34+38+40)/7
= 231/7
= 33
x 26 28 31 34 34 38 40 |
d = x -x̄ and d = x - 33 26-33 = -7 28-33 = -5 31-33 = -2 34-33 = 1 34-33 = 1 38-33 = 5 40-33 = 7 |
d2 49 25 4 1 1 25 49 Σd2 = 154 |
σ = √(Σd²/n)
= √(154/7)
= √22
= 4.690
= 4.69
So, standard deviation of the given data is 4.69.
Question 2 :
Calculate the standard deviation of the following data
x 3 8 13 18 23
f 7 10 15 10 8
Solution :
Let us use actual mean method to find standard deviation.
x 3 8 13 18 23 |
f 7 10 15 10 8 |
d = x - 13 -10 -5 0 5 10 |
d² 100 25 0 25 100 |
fd² 700 250 0 250 800 |
Σf = 50 and Σfd² = 200
σ = √(Σfd²/Σf)
= √(2000/50)
= √40
= 6.32455
= 6.32
So, standard deviation of the given data is 6.32
Question 3 :
The number of books bought at a book fair 200 students from a school are given in the following table.
Number of books 0 1 2 3 4
Number of students 35 64 68 18 15
calculate the standard deviation.
Solution :
x 0 1 2 3 4 |
f 35 64 68 18 5 |
d = x - 2 -2 -1 0 1 2 |
d² 4 1 0 1 4 |
fd² 140 64 0 18 60 |
σ = √(Σfd²/Σf)
= √(282/200)
= √1.41
= 1.18
So, standard deviation of the given data is 1.18
Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
Jul 27, 24 04:58 AM
Jul 27, 24 04:44 AM
Jul 27, 24 04:15 AM