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		7
$30-39		4
$40-49		6
$50-59		4
$60-69		5
$70-79		1
$80-89		3

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.

Sample mean	$
Sample standard deviation	$

Answer 1

Assuming we use the midpoint price of each range (for example, we use 24.5 for 20-29),
Mean = Sum of All Values / Number of Values
= [(24.5 x 7) + (34.5 x 4) + (44.5 x 6) + (54.5 x 4) + (64.5 x 5) + (74.5 x 1) + (84.5 x 3)] / 30
=1445/30

MEAN = 48.166

To find the Standard Deviation:
Step 1: Get Mean. Done above. Mean = 48.166
Step 2: Subtract Mean from Each Value
24.5 - 48.166 = - 23.666
34.5 - 48.166 = - 13.666
44.5 - 48.166= - 3.666
54.5 - 48.166 = 6.334
64.5 - 48.166 = 16.334
74.5 - 48.166 = 26.334
84.5 - 48.166 = 36.334
Step 3: Square each of the values in Step 2

-23.66^2 = 560.079

-13.666^2 = 186.759

-3.666^2 = 13.439

6.334^2= 40.119

16.334^20= 266.799

26.334^2= 693.479

36.334^2 = 1320.159

Step 4: Add up all the numbers in Step 3
SUM OF STEP 3 = 3080.833
Step 5: Multiply the answer from Step 4 by 1/N = 1/30
3080.833 x (1/30) = 102.6944
Step 6: Take the square root of the answer from Step 5
sqrt(102.6944) = 10.1338

Standard Deviation = 10.1338

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