1. What are standard deviation, mean, and variance for sample and populations and what Greek letters represent them? Give examples please.

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1. What are standard deviation, mean, and variance for sample and populations and what Greek letters represent them? Give examples please.

The traditional symbol for the sample standard deviation is S (lowercase or uppercase; there is a slight difference between the two) and the equivalent Greek letter sigma is commonly used to denote the population standard deviation. The greek symbol for the population mean is mu; and the traditional symbol for the sample mean is Xbar (represented by an x with a line over it).

The sample variance is "S" squared and the population variance is sigma squared. These two are probably the ones you will work with the most.

Their mathematical definitions are as follows:

S^2 = Sum(i=1 to n)(X_i - Xbar)^2
---------------------------
n - 1

Where X_i denotes the ith value in our sample, the ith realization of the random variable X, and Xbar, written as a X with a bar above it, denotes the sample mean (again, not to be confused with the population mean).

sigma^2 = E((X - mu)^2)

Where E denotes the expected value function, which you may or may not have encountered already. Roughly, the expected value function tells you the value "on average" that we would expect the expression sent as input to the function to take.

For example, the expected value of the random variable X, E(X), would be the value we expect this variable to take on average, which is nothing more than the population ...

Solution Summary

This solution explains standard deviations, means, and variances for samples and populations, and provides the Greek letter symbols and illustrative examples for each.

Use the data below to answer the determine varianceandstandard deviation. (note: carry your calculator out to 4 decimal places).
Year Actual Return Average Return Deviation for the Mean Squared Deviation
1 .12 .103 .017

Question: A portfolio is made up of 75% of stock 1, and 25% of stock 2. Stock 1 has a variance of .08, and stock 2 has a variance of .035. The covariance between the stocks is -.001. Calculate both the varianceand the standard deviation of the portfolio.

The percentage rates of home ownership for 8 randomly selected states are listed below. Estimate the population varianceandstandard deviation for the percentage rate of home ownership with 99% confidence level.
66.0 75.8 70.9 73.9 63.4 68.5 73.3 65.9
I am attempting to confirm my calculations.

1. Calculate the mean for samples where:
a. n=10 sum of x=85 ?
b. n= 16 sum of x = 400 ?
c. n =45 sum of x =35 ?
d. n=18 sum of x =242 ?
2. Calculate the mean, median, and mode for each of the following samples:
a. 7, -2, 3, 3, 0, 4
b. 2, 3, 5, 3, 2, 3, 4, 3, 5, 1, 2, 3, 4
c. 51, 50, 47, 50, 48, 41, 59, 68, 45,

How may varianceandstandard deviation be applied to a real-world business-related problem? Provide a specific application in which these measures are useful.