Answer to Question #186002 in Statistics and Probability for april rico

Question

In a number series representing X as 3, 6, 8. 7, 9, 3, 4, 6, 6, 8, 6, 4, 3, 7, 4, kindly show clear solutions on the following:

 

a)      what number is the most frequently appearing? how do you call the number?

b)     How many X values are there?

c)      what is ΣX equal to?

d)     what is the n equal to in the number series?

e)      show the longhand of ΣX/n and what is that particularly equal to?

f)       what is the lowest equivalent of n in the above number series if X is equal to each of the values in the series?

g)     what is the highest equivalent of n in the above number series if X is equal to each of the values in the series?

h)     what is the midpoint of this series?

i)       what is ΣX² equal to?

Answer 1

Solution:

Given numbers: 3, 6, 8, 7, 9, 3, 4, 6, 6, 8, 6, 4, 3, 7, 4.

Arranging in ascending order: 3, 3, 3, 4, 4, 4, 6, 6, 6, 6, 7, 7, 8, 8, 9.

a) 6 appears most frequently. It is called mode.

b) X values are 6 ( i.e., 3, 4, 6, 7, 8, 9)

c) ΣX = 3+3+3+4+4+4+6+6+6+6+7+7+8+8+9 = 87

d) n = 15

e) ΣX/n = 87/15 = 5.8

It is called mean.

f) n remains same.

g) n remains same.

h) Mid-point = (n+1)/2 term = 16/2 term = 8th term = 6

i) $ΣX^2=3^2+3^2+3^2+4^2+4^2+4^2+6^2+6^2+6^2+6^2+7^2+7^2+8^2$

$+8^2+9^2=526$