Measures of central tenancy

Variability

A measurement of how spread out the scores are in a distribution. A measure of variability usually accompanies a measure of central tendency for a set of scores. Central tendency describes the central point of the distribution whereas variability describes how the scores are distributed around that central point. Is a method of determining where individual variables are located around the mean. Most often used to measure interval and ratio variables. Can be measured with the range, interquartile range and the standard deviation/variance.

In descriptive statistics the z score would tell you

exactly where that score is in relation to others.

Beyond -2 or +2 =

extreme

Near 0 =

representative

Interquartile range is

the distance covered by the middle 50% of the distribution. Calculate the median of the lower half ( of 9 numbers it would be the first 4) add the 2 middle numbers divided by 2 do the same for the upper half minus the upper from the lower

Standard deviation is

the standard distance between a score and the mean.

Range is

the total distance covered by the distribution - from highest score to lowest.

In inferential statistics the z score would help tell

whether a sample is representative of the population or is extreme or unrepresentative.

Z scores

If a score is transformed into a z score it tells you exactly where it is relative to all other scores in the distribution. The sign of the z score + or - identifies whether X value is located above the mean + or below the mean -. The numerical value of the z score corresponds to the number of standard deviations between X and the mean of the distribution. A Z score of 1.5 means that the observation is 1.5 standard deviations above the mean, whereas a score of −2 means that the observation is 2 standard deviations below the mean. MEAN IS ALWAYS IN THE MIDDLE

Mean

Most common measure of central tendency presented in studies. Average What is the mean? 11, 35, 48, 51, 60, 98

Normal Distribution

Most variables measured in the clinical sciences are approximately normally distributed.

Median

Ordinal, interval or ratio data. Middle number

Normal curve characteristics

Symmetrical Equal number of cases fall above the mean and below the mean Few cases fall into the high or low values of x Mean median and mode are all the same positively skewed would mean the mean and median fall to the right of the mode negatively skewed would mean the mean and median fall to the left of the mode

As a descriptive statistic

Variability measures the degree to which the scores are spread out or clustered together in a distribution.

As an inferential statistic

Variability provides a measure of how accurately any individual score or sample represents the entire population.

Mode

When data is nominal Can also be calculated for continuous data and discrete data Does not take into account scores from the whole distribution. Most frequently occurring number

how to calculate a z score

X value - mean divided by standard deviation