Data-based and Statistical Reasoning (12)

Measures of Central Tendency

provides a single value representation for the middle of a group of data

Arithmetic Mean or Average

is a measure of central tendency that equally weighs all values; it is most affected by outliers

Median

is the value that lies in the middle of the data set. Fifty percent of data points are above and below the median

Mode

is the data point that appears most often; there may be multiple (or zero) of these in a data set

Normal Distribution

is symmetrical. The mean, median, and mode are all the same in the normal distribution

Standard Distrubution

is a normal distribution with a mean of zero and a standard deviation of one; it is used for most calculations. 68% if data points occur within one standard deviation of the mean, 95% within two, and 99% within three

Skewed Distribution

have differences in their mean, median, and mode; the skew direction is the direction of the tail of the distribution

Bimodal Distribution

have multiple peaks, although not necessarily multiple modes, strictly speaking. It may be useful to perform data analysis on the two groups separately

Range

is the difference between the largest and smallest values in a data set

Interquartile Range

is the difference between the value of the third quartile and first quartile; this can be used to determine outliers

Standard Deviation

is a measurement of variability about the mean; this can also be used to determine outliers

Outliers

may be a result of true population variability, measurement error, or a non normal distribution

Independent Events

the probability of this does not change based on the outcomes of other events

Dependent Events

the probability of this changes depending on the outcome of other events

Mutually Exclusive Outcomes

cannot occur simultaneously

Exhaustive

when a set of outcomes is _________, there are no other possible outcomes

Hypothesis Tests

use a known distribution to determine whether a hypothesis of no difference (the null hypothesis) can be rejected

p-value; Significance Level (alpha)

whether or not a finding is statistically significant is determined by the comparison of a _________ to the selected __________

0.05

a significance level of ______ is commonly used

Confidence Intervals

are a range of values about a sample mean that are used to estimate the population mean

Confidence Level

a wider interval is associated with a higher _________ (95% is common)

Pie Charts (Circle Charts) and Bar Charts

are both used to compare categorical data

Histograms and Box Plots (Box-and-whisker Plots)

are both used to compare numerical data

Maps

are used to compare up to two demographic indicators

Linear, Semilog, and Log-log Plots

can be distinguished by their axes

Slope

can be calculated most easily from linear plots

Tables

may contain related or unrelated categorical data

Correlation and Causation

are separate concepts that are linked by Hill’s criteria