Chapter 3: Describing Data: Numerical Measures

Statistic

The mean of a sample, or any other measure based on sample data

The mode

The value of the observation that appears most frequently .

Major properties of the median are

1. Is it not affected by extremely large of small values. 2. It can be computed for ordinal-level data or higher.

Geometric mean

Useful when finding the average change of percentages, ratios, indexes or growth rates over time.

A symmetrical distribution

When all three means of location are at the center of the distribution.

Variance

It measures the mean amount by which the values in a population, or sample, vary from their mean.

The properties of arithmetic mean

1. To compute a mean, the data must be measured at the interval or ratio level. 2. All the values are included in computing the mean 3. The mean is unique which means there's only one mean in a set of data 4. The sum of the deviations of each value from the mean is zero

Weighted mean

A convenient way to compute the arithmetic mean when there are several observations of the same value. ex: $1.84 + $1,84 + $2.07 + $2.40 + $2.40 DIVIDED by 5 (total of samples)

Measure of dispersion

A value that shows the spread of a data set. The range, variance and standard deviation are measures of dispersion. Is to pinpoint the center of a distribution of data.

Arithmetic mean

A widely used measure of location. It has several properties (four to be exact)

Empirical rule

For a symmetrical, bell-shaped frequency distribution, approximately 68% of the observations will lie within plus and minus one standard deviation of the mean, about 95% of the observations will lie within plus and minus two standard deviations of the mean and practically all (99.7.%) will lie within plus and minus three standard deviations of the mean.

Chebyshev's Theorem

For any set of observations (sample or population), the proportion of the values that lie within k standard deviations of the mean is at least 1 - 1k^2, where k is any value greater than 1

Range

Range = Max. value - Min. value

Measures of location

Referred to as averages. - ex: The average U.S. homes changes ownership every 11.8 years.

Sample mean

The mean is the sum of all the sampled values divided by the total number of sampled values. ** look at notebook for formula

Median

The midpoint of the values after they have been ordered from the minimum to the maximum values. - must be at least an ordinal level of measurement

Population mean

The sum of all the values in the population divided by the number of values in the population. ** look at notebook for formula