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
