Introduction to Statistics Chapter 4-5

Weighted Mean Formula

/X = W1X1+ W2X2 +.....+WN+XN/W1+W2....+WN

Arithmetic Mean Formula

1/N(X1 + X2 +...+XN)

Outlier

A data value that is extremely different from other measurements in a data set

Resistant Outlier

Statistical Measures not affected by outliers

Deviation

X-A is how far X deviates from A is also called a Deviation

Mediean

a set of observations is the measure of the center that is the middle value of the data when it is arranged in ascending order. The same number of data values lie on ether side of the median.

Range

difference between the largest and smallest data values

Mode

is a data set is the most frequently occuring value

trimmed mean

is a modification of the arithmetic mean which ignores an equal percentage of the highest and lowest data values in calculating the mean. As expected the trimmed mean is not affected by the addition of an outlier, while the mean increased dramatically. This is why the trimmed mean is considered to be a resistant measure

Standard Deviation

is also a measure of how much data varies around the mean. It is found by taking the square root of the variance

Moving Average

is obtained by adding consecutive observations for a number of periods and dividing the number of periods included in the average

Proportion

of any data set lying within K standard deviations of the mean is at least 1-1/k2 for k>1