Verify that a maiority of all weights fall within one standard deviation of the

Question

Verify that a maiority of all weights fall within one standard deviation of the mean (169 51) and that a small minority of all weights deviate more than two standard deviations from the mean. In what sense is the variance a type of mean? not a readily understood measure of variability? a stepping stone to the standard deviation? Specify an important difference between the standard deviation and the mean. Why can't the value of the standard deviation ever be negative? Indicate whether each of the following statements about degrees of freedom is true or false. Degrees of freedom refer to the number of values free to vary in the population.

Explanation / Answer

4.16 )

Mean

The mean value or score of a certain set of data is equal to the sum of all the values in the data set divided by the total number of values. A mean is the same as an average. For example, if a certain data set consists of the numbers 2, 5, 5, 8 and 10, the sum of the numbers is 30. Since there are five total numbers in the data set, the mean of the set is equal to 6 because 30 divided by 5 equals 6.

Standard Deviation

Standard deviation is a statistical measurement of the variation in a set of data. Standard deviation indicates how much the values of a certain data set differ from the mean on average. In a normal distribution -- where data is roughly equally distributed -- about 68 percent of data points lie within one standard deviation of the mean and 95 percent of values lie within two standard deviations of the mean. For example, if the mean score on a certain standardized test is 1,200 and the standard deviation of scores is 100, you would expect 95 percent of test takers to get a score within two standard deviations of the mean, or between 1,000 and 1,400.

4.17)

Variance is squared, removes the negative, and standard dev is obviously the square root of variance which makes it impossible to have a negative standard deviation.

Standard deviation can be zero, but never negative. Both sides of the distribution result in positive value for standard deviation.

4.18)

a) True

degrees of freedom=number of indepent pieces - 1

b)

true:

we loose one df if we calculate any parameters like mean, variance etc.,

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