Question

The following frequency distribution shows the price per share for a sample of 30 companies listed on the New York Stock Exchange. Price per Share                         Frequency $20-29                         5 $30-39                         5 $40-49                         7 $50-59                         4 $60-69                         6 $70-79                         2 $80-89                        
1 Compute the sample mean price per share and the sample standard deviation of the price per share for the New York Stock Exchange companies (to 2 decimals). Assume there are no price per shares between 29 and 30, 39 and 40, etc.
What is the Sample mean $
What is the Sample standard deviation $

Answer 1

Answer)

We have

20-29. 5

30-39. 5

40-49. 7

50-59. 4

60-69. 6

70-79. 2

80-89. 1

Now we need to take the mid points of the values

24.5, 34.5...

Now we need to multiply them with their respective frequencies and add them

= (24.5*5) + (34.5*5)...

= 1445

Now we need to divide the result by sample.size = 30

Mean = 1445/30 = 48.167 = 48.17

To find the standard deviation

First we need to subtract mean from each and every mid point then we need to square them and multiply them with their respective frequency and atlast add them

5*(24.5-48.17)^2 + 5*(34.5-48.17)^2....

= 8296.667

Now, we need to divide the sum by sample size -1 that is by 29

And take the square root of the result

Sample standrad deviation = √{(8296.667/29)

= 16.914

= 16.91