Statistical Techniques in Business & Economics Chapter 3

Positively skewed distribution

Arithmetic mean is the largest of the three measures; skewed to the right

Sum of midpoint of each class times frequency of that class / number of frequencies

Arithmetic mean of grouped data

Mean= 38 Variance= 82.667 SD= 9.0921

Based on a sample, the following are times, in minutes, required to install 10 door openers: 28, 32, 24, 46, 44, 40, 54, 38, 32, and 42. Compute the mean, variance and SD.

Square root of population variance

Population standard Deviation formula

Sum of each value minus the mean squared / number of values

Population variance

End value divided by beginning value taken to the root of which years that passed

Rate of increase over time formula

Sum of values / number of values

Sample mean formula

Square root of sample variance

Sample standard deviation formula

Sum of each value minus the mean squared / number of value minus one

Sample variance

Sum of frequency of each class times each class midpoint minus the mean squared / number of frequencies minus 1

Standard deviation of grouped data

1Sd 68% 2SD 95% 3SD 99.7%

Empirical rule lies

Parameter

characteristics of a population

Variance

A measure of dispersion based on the average squared differences from the arithmetic mean.

Measure of location

A single value that is typical of the data. It pinpoints the center of a distribution. The arithmetic mean, weighted mean, median, mode, and geometric mean are measures of location

Measure of dispersion

A value that shows the spread of a data set. The Range, Variance, and Standard Deviation are measures of dispersion.

1- 1/number standard deviations squared

Chebyshevs theorem formula

Mean= 4 Variance= 5.5 SD= 2.3452

Consider these values a sample: 7, 2, 6, 2, and 3. Compute the mean, variance, and SD.

Weighted Mean

Each value is weighted according to its relative importance.

Coefficient of determination

Explicates how well data points fit a line or curve. (prediction of future outcomes)

Chebyshev's Therom

For any set of observations the proportion of the values that lie within K standard deviations of the mean is at least 1-1k^2

Arithmetic mean

The sum of the values divided by the number of values.

Each percentage change (.3 would be 1.3) multiplied together and the the total number of percentages root is taken out

Geometric mean formula

Range

It is a measure of dispersion. The range is found by subtracting the minimum value from the maximum value

Median

The value of the middle observation after all the observations have been arranged from low to high.

Mean= 95.1 Variance= 123.66 SD= 11.12

Listed below are the room rates for business-class guests for a sample of 10 motels: 101, 97, 103, 110, 78, 87, 101, 80, 106, 88. Compute the mean, variance, and SD.

Coefficient of variation

Measure of dispersion of data points in a data series around the mean

Skewed distribution

Nonsymmetrical; relationship among three measures changes.

Sum of values / numbers of values

Population mean formula

Negatively Skewed

The mean is the lowest of the three measures; skewed to the left

Mean deviation

The mean of the deviations from the mean, disregarding signs.

Geometric mean

The nth root of the product of all the values.

Standard Deviation

The square root of the variance.

Mode

The value that appears most frequently in a set of data.

Sum of each weight times that weights frequency / sum of all frequencies

Weighted mean formula

Statistics

characteristics of a sample