Stat: Chapter 3 09/10/2013
Central tendency▯ the extent to which the data values group around a typical or central value
Arithmetic mean (sum)/(number of values) “balance point”
Sample mean▯ sum of the values in a sample divided by the number of values in the sample
When there are extreme numbers avoid using the mean
Median ▯ value in center of data marked smallest to largest
Not affected by extreme values (n+1)/(2)
Mode is the value in a set of data that appears most frequently
Not affected by extreme data
Variation▯ is the amount of dispersion or scattering of values away from a central value
Measures the spread or dispertion, ex. Range, standard deviation and variance
Range measures he total spread in the set of data, does not tae into account how the data are distributed
Variance and stand dev. Measure the average scatter around the mean how larger numbers fluctuate above
and lower numbers fluctuate below
Sum of squares (SS) ▯ difference between each value and the mean and then sums these squared
differences. This sum is then divided by the number of values minus one, to get the sample variance. The
square root of the sample variance is the stand dev.
As the sample sie increases the difference between dividing byn and by n – 1 becomes smaller and
Sample stand of dev as a measure of variation
If the number in a data set are all the sme there is no variance and stand dev will be 0
Coefficient of variation ▯ relative measure of variation that is expressed as a percentCV) measures
the scatter in the data relative to the mean. Equal to the stand dev divided by the mean multiplied by 100
CV = (S/X)z00%
The shape is the pattern of the distribution of values from the lowest value to the highest value
Extreme or outlier value is located far from the mean
The Z score, which is the difference between the value and the mean divided by the stand deviation
Z = (x – xbar)/S
Shape▯ is the pattern of distribution of data values throughout the entire range of all the values.
A symmetrical distribution▯ the values below the mean are distributed in exactly the same way as the
values above the mean. (skewness of 0) Skewed distribution ▯ the values are not symmetrical around the mean. The skewness result in an
imbalance of low values of high values.
Shape can influence the relationship of the mean to the median.