Quiz two Flashcards
What does variability measure as a descriptive statistic?
The degree to which the scores are spread out or clustered together in a distribution
What does variability measure in the context of inferential statistics?
How accurately any individual score or sample represents the entire population
Small variability versus large variability
A population with a small variability will have scores clustered close together, and any individual score or sample will necessarily provide a good representation of the entire set
Large variability means courses are widely spread, and it is easy for one or two extreme scores to give a distorted picture of general population
Three measures of variability
Range, standard deviation, variance
And in each case, variability is determined by measuring distance
Define range
The total distance covered by the distribution, the highest score to the lowest score
Formula for range
Largest value minus smallest value
What does standard deviation measure?
The standard distance between a score and the mean
Sample standard deviation equation
S= the square root of ((sigma(x-x)^2/ n-1))
What does it mean to have a higher standard deviation?
Higher spread less consistency and clustering
Steps to solve standard deviation
- Find the distance from the mean for each score.
- Square each deviation.
- Compute the mean of the square deviations. (some squares divided by N.)
- For samples divided by N minus one.
- Take the square root of the variance to obtain the standard deviation.
Define variance
A measure of how data points differ from the mean
How to get standard deviation from variance
Take the square root of it
Which measure of dispersion is most affected by extreme outliers
Range
What is the point of displaying your data visually?
Much more effective way of examining characteristics of a distribution as well as characteristics of any data set
Allows us to see patterns and trends , is understandable and digestible
Difference between bar, chart and histogram
A bar graph is for categorical data (nominal, and ordinal)
A histogram is for a distribution frequency (ratio, and interval)
If you were looking at frequency of class standing, you could use a
Pie chart and bar chart (nominal ordinal)
If you were looking at frequency of class scores, you could use a
Histogram (interval)
Define frequency distribution
A representation either in a graphical or tubular format that displays the number of observations within a given interval
Rules for frequency distribution(5)
- Intervals, exclusive, and exhaustive.
- Determine the range.
- Select a class interval , maximum 10 to 20 intervals
- Commute the range and divide by the number of intervals you want.
- Decide on starting point and create intervals.
Define histogram
Visual representation of distribution where frequencies are represented by bars
Define frequency polygon
Graph plotting the frequencies of the different data values on the vertical access and then connects to the plotted points with straight lines
Difference between frequency, polygon, and cumulative frequency polygon
Frequency polygon: graph that shows the individual frequency of each class interval by plotting midpoint and connecting the points with lines
Cumulative frequency polygon : a graph that shows the cumulative frequency of each class interval by plotting the cumulative totals and connecting the points with lines
Give an example why a pie chart might be useful
Good for showing proportions and percentages for nominal and ordinal data
What is the most intervals you should typically have in a graph
10 to 20
