I'll be honest. *Standard*** deviation** is a more difficult concept than the others we've covered. And unless you are writing for a specialized, professional audience, you'll probably never use the words "

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*Standard*** Deviation**
objective
• Describe

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** Deviation**
Definition:
Behavior commonly seen in children that is the result of some obstacle to normal development such behavior may be commonly understand as negative (a timid child, a destructive child) or positive (a quite child), both positive and negative

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Mean and *Standard*** Deviation**
The mean, indicated by μ (a lower case Greek mu), is the statistician's jargon for the average value of a signal. It is found just as you would expect: add all of the samples together, and divide by N. It looks like this in mathematical form:
In words, sum the values in the signal, xi, by letting the index, i, run from 0 to N-1. Then finish the calculation by dividing the sum by N. This is identical to the equation: μ =(x0 + x1 + x2 + ... + xN-1)/N. If you are not...

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selected.
c) reasonably large due to the “cluster” effect.
d) 100 divided by the size of the population of Laramie.
Costs for ** standard** veterinary services at a local animal hospital follow a Normal distribution with a mean of $80 and a

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milligrams of tar per cigarette and a *standard*** deviation** equal to 1.0 milligram. Suppose a sample of 100 low-tar cigarettes is randomly selected from a day’s production and the tar content is measured in each. Assuming that the tobacco company’s claim is true, what is the probability that the mean tar content of the sample is greater than 4.15 milligrams?
[0.00621]
2. The safety limit of a crane is known to be 32 tons. The mean weight and the

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the mean from part b find the *standard*** deviation** of the probability distribution.
8. A computer password consists of two letters followed by a five-digit number, none of which can be repeated. After 3 tries the computer locks down and notifies security.
a) What is the probability of guessing the correct password on the first try?
b) What it the probability of guessing the correct password within three tries?
9. Find the mean and

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the actuarial field and finds the average salary to be $41,000. The population *standard*** deviation** is $3000. Can her claim be supported at 0.05?
x¯=14.7, μx¯=13.77, ox¯=5.34, n=29, α=.01
3. Monthly Home Rent. The average monthly rent for a one bedroom in San Francisco is $ 1229. A random sample of 15 one bedroom homes about 15 miles outside of San Francisco had a mean rent of $1350. The population

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9551/SQRT(300),1) = 0.0783
(c) A circuit contains three resistors wired in series. Each is rated at 6 ohms. Suppose, however, that the true resistance of each one is a normally distributed random variable with a mean of 6 ohms and a *standard*** deviation** of 0.3 ohm. What is the probability that the combined resistance will exceed 19 ohms? How "precise" would the manufacturing process have to be to make the probability less than 0.005 that the combined resistance of the circuit would exceed 19...

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Sales Price | | Days to Sell | |
| | | | | |
Mean | 474007.5 | Mean | 454222.5 | Mean | 106 |
** Standard** Error | 31194.293 |

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in analysing the data is determining if outliers exists within the data. The presence of outliers must be evaluated because their existence could distort the data and make it inaccurate. In order to determine if outliers exist the average and *standard*** deviation** must be calculated in order to calculate the Z score, which will show, wither or not outliers exist. In this instance to outliers where found present in the data set as all of the data fell within the +3,-3 range, the largest positive outlier...

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corresponds to a 94% level of confidence.
A. 1.88
B. 1.66
C. 1.96
D. 2.33
2. In a sample of 10 randomly selected women, it was found that their mean height was 63.4 inches. Form previous studies, it is assumed that the *standard*** deviation**, σ, is 2.4. Construct the 95% confidence interval for the population mean.
A. (61.9, 64.9)
B. (58.1, 67.3)
C. (59.7, 66.5)
D. (60.8, 65.4)
3. Suppose a 95% confidence interval for µ turns out to be (120, 310). To make...

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*Standard*** Deviation** Abstract
QRB/501

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14, 14, 15, 15, 16. The mean is 14.0mm.What is the best estimate of the *standard*** deviation**?
-1mm
5 1000 bananas were collected from a single plantation and weighed.Their masses formed a normal distribution. How many bananas would be expected to be within 2

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*Standard*** deviation** can be difficult to interpret as a single number on its own. Basically, a small

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and variability (*standard*** deviation**) of Reynolds, Hasbro, and Vanguard Index 500 Trust during the past 5 years. Which one appears to be riskiest?
S&P 500
REYNOLDS
HASBRO
Mean
0.57%
1.87%
1.18%
Variance
0.13%
0.88%
0.66%

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and *standard*** deviation** of the probability distribution created by rolling a die. Either show work or explain how your answer was calculated.
Descriptive Statistics: Die1 Variable Mean StDevDie1 3.450 1.317Mean: 3.50

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For the ** standard** normal probability distribution, the area to the left of the mean is
a.
–0.5
c.
any value between 0 to 1
b.
0.5
d.
1
Answer: B
The total area under the curve is 1. The area on the left is the half of 1 which is 0.5.
____ 2. Which of the following is not a characteristic of the normal probability distribution?
a.
The mean and median are equal
b.
The mean of the distribution can be negative, zero, or positive
c.
The distribution is symmetrical
d.
The

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$3,291.00 up to $15,906.00 for the period of the said year. Its average price is $6,165.26 with a *standard*** deviation** of $2,949.50. It can be seen that prices are not close by to one another.
With regards to mileage, the majority of the automobiles runs 41 miles for every gallon of gasoline, while the least runs only for 12 miles. The mean of mileage has resulted to 21.30 mpg, with a

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many normal distributions. Normal distributions can differ in their means and in their *standard*** deviations**. Figure 1 shows three normal distributions. The green (left-most) distribution has a mean of -3 and a

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Tensile testing of thermoplastics
** Standards**: AS 1145 (Australian

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| 1.0056 |
32 | 1.0058 |
33 | 1.0061 |
The *standard*** deviation** value represents the average distance of a set of scores from the mean. It statistical measure of the precision for a series of repetitive measurements. The sample

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following returns and corresponding probabilities for asset A, compute its *standard*** deviation** and coefficient of variation.
Answer:
SD = 3.87%
CV = SD/K = 3.87/15 = 0.26
Champion Breweries must choose between two asset purchases. The annual rate of return and related probabilities given below summarize the firm's analysis.
5. For each asset, compute
(a) the expected rate of return.
(b) the

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confidence intervals verses point estimates? The sample mean is a point estimate (single number estimate) of the population mean – Due to sampling error, we know this is off. Instead, we construct an interval estimate, which takes into account the *standard*** deviation**, and sample size.
– Usually stated as (point estimate) ± (margin of error)
• What is meant by a 95% confidence interval? That we are 95% confident that our calculated confidence interval actually contains the true mean.
• What is the...

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Mean, median, mode and *standard*** deviation** of Allium cepa cells and Ovibos moschatus Oculi cells
| Allium cepa cells | Ovibos moschatus Oculi cells |
Mean / m | 296.0 | 29.0 |
Median / m | 300.0 | 30.0 |
Mode / m | 320.0 | 30.0 |

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+ (0.20) (0.15) + (0.40)(0.20) + (0.20) (0.25) + (0.10) (0.30)
= 0.20 or 20%
5. The risk of a single asset is measured by its *standard*** deviation** or coefficient of variation. The

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measurements.
Section 7.1 Turning Data into Information
Four kinds of useful information about a set of data: center, variability, shape and outlier
Types of center: mean, median and mode (and their definitions)
Types of variability: range, *standard*** deviation** and IQR (and their definitions)
Types of shape: symmetric, skew to the left, skew to the right, unimodal and bimodal (and their definitions)
Definition of outlier (unusual values):
Section 7.2 Picturing Data
Stem-and-leaf plot and how to...

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the products they liked. This effect was only due to the customer's mood during the time of purchase.
In an attempt to understand the impact of brand loyalty on consumers, Bhattacharya (1997) investigated the factors that relate to the ** deviations** of brand loyalty in markets. He looked at measures of brand loyalty against category requirements used by consumers (i.e.: norms of a product and the appropriate location in the store). The study finds that on average, brands that cater to some...

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[ασ (RA ) − (1 − α)σ (RB )]2 .
Therefore, the *standard*** deviation** of portfolio P is
σ (RP ) = ασ (RA ) − (1 − α)σ (RB ).
As assets A and B are perfectly negatively correlated, we can construct portfolio P
such that its

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(d)
H0 : μ = 4.4
H1 : μ < 4.4
4.35
0.18
0.02
100
3. A teacher claims that students in Class A put in more hours studying compared to other students. The mean numbers of hours spent studying per week is 25 hours with a *standard*** deviation** of 3 hours per week. A sample of 27 Class A students was selected at random and the mean number of hours spent studying per week was found to be 26 hours. Can the teacher’s claim be accepted at 5% significance level?
4. Trying to encourage...

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02+16.04+16.05+16.01+16.02+16.02+16.03+16.01+16+16.07)/12=16.03
(b) Calculate the sample *standard*** deviation**.
=0.0193
3.2. The bore diameters of eight randomly selected bearings are shown here (in mm): 50.001, 50.002, 49.998, 50.006, 50.005, 49.996, 50.003, 50.004
(a) Calculate the sample average.
(50.001+50.002+ 49.998+50.006+50.005+49.996+50.003+50.004)/8=50.001
(b) Calculate the sample

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curve within plus and minus two *standard*** deviations** of the mean and practically all (99.73 percent) of the area under the normal curve is within three

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price
Annual dividend
High growth
£68
£2.5
Normal growth
£54
£1.5
No growth
£45
£0.5
Assuming all three scenarios are equally likely, calculate:
a) the expected holding-period return;
b) the variance and *standard*** deviation** of the holding-period return;
c) the expected return and

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values.
*Standard*** Deviation**
The

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which the performance
of portfolio in a given period of time is measured.
In Sharpe index, three things must be known:
the portfolio return,
the risk free rate of return - use the average return
(over the given period of time).
the *standard*** deviation** of the portfolio – it is
measure the systematic risk of the portfolio.
The ratio describes how much excess return you are
receiving for the extra volatility that you endure for
holding a riskier asset
Properly compensated for the additional...

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Unfortunately, your small firm cannot afford the expensive databases that would provide all this information with a few simple keystrokes, but that’s why they hired you. Specifically, you have been asked to determine the monthly average returns and *standard*** deviations** for the 12 stocks for the past five years.
The stocks (with their symbols in parentheses) are:
Apple Computer (AAPL) Hershey (HSY)
Archer Daniels Midland (ADM) Motorola...

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the expected *standard*** deviation** for XYZ stock?
4.
A T-bill pays 6 percent rate of return. Would risk-averse investors invest in a risky portfolio that pays 12 percent with a probability of 40 percent or 2 percent with a probability of 60 percent? A) Yes, because they are rewarded with a risk premium. B) No, because they are not rewarded with a risk premium. C) No, because the risk premium is small. D) Cannot be determined. E) None of the above
5. In the mean-

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distinguish between the two in order to use the correct formula? mean; median; mode; range; quartiles; variance; *standard*** deviation**. 2. The following numbers represent the weights in pounds of six 7year old children in Mrs. Jones' 2nd grade class. {25, 60, 51, 47, 49, 45} Find the mean; median; mode; range; quartiles; variance;

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Complete Parts A, B, and C below.
Part A
1. Why is a z score a ** standard** score? Why can

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determined from historical records that demand for sand during leadtime averages 50 tons. In addition, suppose the manager determined that the demand during leadtime could be described by a normal distribution that has a mean of 50 tons and a *standard*** deviation** of 5 tons. Answer the following questions, assuming that the manager is willing to accept a stockout risk of no more than 3 percent:
a) What value of z is appropriate?
b) How much safety stock should be held?
c) What reorder point should...

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client can quickly learn whether the process is operating satisfactorily or corrective actions needs to be taken.
Summary of Statistics
Sample 1
Sample 2
Sample 3
Sample 4
Mean
11.96
12.10
12.14
12.15
** Standard** Error
0.04
0.04
0.04
0.02

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and a *standard*** deviation** of 0.018 inch. The customer will buy only those pins with lengths in the interval inch. In other words, the customer wants the length to be 1.00 inch but will accept up to 0.02 inch

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We can do a lot of good statistics with the normal curve, but virtually none with any other curve.
Let us assume that we have recorded the 1000 ages and computed the mean and *standard*** deviation** of these ages. Assuming the mean age came out as 40 years and the

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intelligence test is 100, and the *standard*** deviation** is 16. The mean for the creativity test is 115, and the

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organization, analysis, interpretation, and presentation of data. It provides a more accurate way of expressing data rather than mere observation. This experiment used the different statistical concepts such as the Q test, mean, *standard*** deviation**, relative

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Fall 2011 - MGMT 305 - Quiz 1 Multiple Choices (1 point each)
Name: ___________________________________________ ID: _______________________
____ 1. The *standard*** deviation** of a sample of 100 observations equals 64. The variance of the sample equals
a. 8
b. 10
c. 6400
d. 4,096
____ 2. The weights (in pounds) of a sample of 36 individuals were recorded and the following statistics were calculated.
mean = 160
range = 60
mode = 165
variance = 324
median = 170
The coefficient...

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Customer Service
…………………..
The 3 year risk is a statistical measure of the month-to-month ups and downs of a fund's returns. Money market funds, which have stable asset values, have *standard*** deviations** close to zero. Volatile, aggressive, growth funds can have

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/ N
* Population *standard*** deviation** = σ = sqrt [ Σ ( Xi - μ )2 / N ]
* Population variance = σ2 = Σ ( Xi - μ )2 / N
* Variance of population proportion = σP2 = PQ / n
* Standardized score = Z = (X - μ) / σ
* Population correlation coefficient = ρ = [ 1 / N ] * Σ { [ (Xi - μX) / σx ] * [ (Yi - μY) / σy ] }
Statistics
Unless otherwise noted, these formulas assume simple random sampling.
* Sample mean = x = ( Σ xi ) / n
* Sample

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the *standard*** deviation** for large company stocks over this period was:

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1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Click on Stat.
Click on Basic Statistics.
Click on Display Descriptive Statistics We need to get a value for the *standard*** deviation** in order to
conduct the test.
Double-click FILL.
Click the OK button (note the value for the sample

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|0.466 |Accepted |
C. Reported Values
Different statistical parameters were solved including the mean (x), *standard*** deviation** (s), relative

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interval measurement.
Descriptive statistics are used because in most cases, it isn't possible to present all of your data in any form that your reader will be able to quickly interpret. The mean, the mode, the median, the range, and the *standard*** deviation** are all examples of descriptive statistics. The mean, median, and the mode are all measures of central tendency. They attempt to describe what the typical data point might look like. In essence they are all different forms of 'the average.'...

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6. What information must you input to a computer program in order to derive theportfolios that make up the efficient frontier
u. Expected returns, Covariances and correlations.
v. *Standard*** deviations**, variances and Covariances.
w. Expected returns,

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from its mean is called the ** deviation** from the mean.
* •If the data is tightly packed around the mean, the

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Analysis
1.
All Sales | Inside | | Outside | |
| | | | | |
Mean | 64925 | Mean | 59289 | Mean | 70562 |
** Standard** Error | 989 |

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tendencies could be very misleading. The measure of dispersion will describe the spread of the data and the variation around the central value. There are two measures of dispersion, variance (range) and *standard*** deviation**. A common measure of dispersion is using the

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of 25% (Anderson, Sweeney, & Williams, 2012).
The measure of variability is expressed through an element of dispersion across a population sample. Variability is measured through the calculation of range, interquartile range, variance, *standard*** deviation**, and coefficient of variation. The range is not commonly used as it is influenced significantly by outliers; however, it is measured by the subtracting the smallest value by the largest value. Interquartile range represents the difference...

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quartile = 3 (50 + 1) / 4 = 38.25 => 5.57
B) Compute the range, interquartile range, variance, *standard*** deviation**, and coefficient of variation.
Range = X largest – X smallest = 5.77 – 5.25 => 0.52
Interquartile range = quartile 3 – quartile 1 = 5.57 – 5.44 => 0.13
Variance = 0.011

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Material
Week Two Practice Problems
Prepare a written response to the following questions.
Chapter 2
12. For the following scores, find the mean, median, sum of squared ** deviations**, variance, and

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expectations realistic? Please explain.
Below is the table (Table 4) which includes the expected return and the *standard*** deviations** for equal investments in High-Tech and Counter-Cyclical stocks. Expected value is 0,0545 and the

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