# Standard Deviation and Frequency Distributions

**Topics:**Standard deviation, Normal distribution, Variance

**Pages:**5 (968 words)

**Published:**November 19, 2012

Frequency Distributions

Module 3/Case

10/148/2012

Professor Kuleshov

Frequency Distributions

This assignment is based on Frequency Distributions and will include the following information: 1.The ability to describe the information provided by the Standard Deviation. 2.The ability to use the Standard Deviation to calculate the percentage of occurrence of a variable either above or below a particular value. 3.The ability to describe a normal distribution as evidenced by a bell shaped curve as well as the ability to prepare a distribution chart from a set of data (module 3 Case).

Part 1

(1) To get the best deal on a CD player, Tom called eight appliance stores and asked the cost of a specific model. The prices he was quoted are listed below: $ 298 $ 125 $ 511 $ 157 $ 231 $ 230 $ 304 $ 372 Find the Standard deviation $ 298 + $ 125+ $ 511+ $ 157+ $ 231+ $ 230+ $ 304+ $ 372= 2228/8 = 278.5(subtract from #s) 19,-153, 232, -121, -47, -48, 25, 93 (square numbers)

380, 2356, 54056, 14762, 2256, 2352, 650, 8742 = 106(added)

(Divide by 7) 15251 (take square root) Standard Deviation = approximately 123. (2) When investigating times required for drive-through service, the following results (in seconds) were obtained. Find the range, variance, and standard deviation for each of the two samples, and then compare the two sets of results. Wendy's 120 123 153 128 124 118 154 110

MacDonald's 115 126 147 156 118 110 145 137

(2) Set 1:

Range : maximum - minimum = 154-110= 44

Number of cases 8

To find the mean, add all of the observations and divide by 8 Mean 125

Squared deviations

(120-125)^2 = (-5)^2 = 25

(123-125)^2 = (-2)^2 = 4

(153-125)^2 = (28)^2 = 784

(128-125)^2 = (3)^2 = 9

(124-125)^2= (-1)^2= 1

(118-125)^2 = (-7)^2 = 49

(154-125)^2 = (29)^2 = 841

(110-125)^2 = (-15)^2 = 225

Add the squared deviations and divide by 8

Variance = 1938/7

Variance = 276

Standard deviation = sort(variance) = 16

Set 2:

Range : 156-110 =46

Number of cases 8

To find the mean, add all of the observations and divide by 8 Mean 131

Squared deviations

(115-131)^2 = (-16)^2 = 280

(126-131)^2 = (-5.75)^2 = 33

(147-131)^2 = (15)^2 = 232

(156-131)^2 = (24)^2 = 588

(118-131)^2 = (-13)^2 = 189

(110-131)^2 = (-21) ^2 = 473

(145-131) ^2 = (13) ^2 = 175

(137-131) ^2 = (5) ^2 = 27

This is divide by 7 because this is a sample data n-1=7

Add the squared deviations and divide by 7

Variance = 1999/7

Variance = 285

Standard deviation = sort (variance) = 16

The standard deviation for restaurant B is slightly smaller than that of restaurant A. The range for restaurant A is slightly less the range of B. This shows there is a little more variation in restaurant A with respect to times required for drive through service than in required for drive through service than in B.

(3) A company had 80 employees whose salaries are summarized in the frequency distribution below. Find the standard deviation. Find the standard deviation of the data summarized in the given frequency distribution. Salary Number of Employees

5,001 -10,000 14

10,001 - 15,000 13

15,001 - 20,000 18

20,001 - 25,000 18

25,001 - 30,000 17

The chart gives frequency and salary, traditional formulas cannot be used due to we do not know the actually salary of each employee. In order to do these assumptions need to be done with using middle point. Example (10000-5001) /2 then added to 5001= 7500

5,001- 10,000 =7500

10,001-15000=12500

15001-20000=17500

2001-2500=22500

25001-30,000=27500

Total number of employees = 80

14, 13, 18, 18, 17= 80

Compute the Mean

14 * 7500 = 105000

13* 12500 = 162500

18* 17500 = 315000

18* 22500= 405000

17 * 27500 = 467500

467500

80

Add up all frequency Mark values Total= 1455000

1455000

80

1455000 / 80 = 18187.5 = 18188

Now standard deviation

Total employees 80

Total 1455000

Means=...

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