Ch.2 Frequency Distributions
Construct a Histogram from a Grouped Frequency Table
1. Determine the midpoint of each interval. 2. Draw the x-axis labelled with the variable of interest and thte midpoints for each interval on this variable. 3. Draw the y-axis, label it "Frequency", and include the full range of frequencies for this variable. 4. Draw a bar for each midpoint, centering the bar on that midpoint on the x-axis and drawing the bar as high as the frequency for that interval.
Steps to Create a Frequency Table
1. Determine the min. and max. scores. 2. Create two columns and label the first with the variable name and the second "frequency" 3. List the *full range* of values from the data set from highest to lowest (include ALL values) 4. Count the number of scores at each value and list them in the frequency column.
Constructing a Hisitogram Using a Frequency Table
1. Draw the x and y axes; label the x-axis with the variable of interest and label the y-axis "frequency" 2. The lowest numbers start where the axes intersect and numbers increasing moving right along the x-axis. - Having 0 at the origin is ideal but if the range of numbers on either axis is far from 0, you can use a different number. 3. Each bar is *centered on* the value for which it provides the frequency.
Steps to Create a Grouped Frequency Table
1. Find the min. and max. 2. Get the full range of data 3. Determine the number of intervals (most often 5 or 10) and the best interval size (rounded to the nearest whole number.). 4. Figure out the number that will be the bottom of the lowest interval. (must be a multiple of the interval size.) 5. List the intervals from highest to lowest and then count the numbers in each.
Histogram
A graph that looks like a bar graph but depicts just one variable, usually based on scale data, with the values of the variable on the x-axis and the frequencies on the y-axis. - difference between histogram and bar graph is that bar graphs provide scores for nominal data (e.g. men vs. women) relative to another variable and a histogram typically provides frequencies for one scale variable - each bar is *centered on* the value for which it provides the frequency.
Frequency Polygon
A line graph, with the x-axis representing values (or midpoints of intervals) and the y-axis of representing frequencies; a dot is placed at the frequency for each value (or midpoint), and the dots are connected.
Normal Distribution
A specific frequency distribution that is a bell-shaped, uni-modal curve.
Grouped Frequency Table
A visual depiction of data that reports frequencies within a given interval rather than the frequencies for a specific value. - solves the issue of having an enormous amount of unnecessary work and allows us to better see trends in the data.
frequency table
A visual depiction of data that shows how often each value occurred; that is, how many scores were at each value. - values are listed in one column and the number of individuals with scores at that value are listed in the second column. - the data in a frequency table can be graphed in a *frequency polygon* or a *frequency histogram*. - it is the best way to create an easy-to-understand distribution of data.
Ceiling Effect
Is a situation in which a constraint prevents a variable from taking on values above a given number.
Skewed Distributions
The distribution in which one of the tails of the distribution is pulled away from the center.
raw score
a data point that has not yet been transformed or analyzed
frequency distribution
describes the pattern of a set of numbers by displaying a count or proportion for each possible value of a variable.
Positively skewed
distributions tail extends to the right, in a positive direction - occurs sometimes when there is a floor effect. mean>median>mode
Floor Effect
situation in which a constraint prevents a variable from taking values below a certain point
Negatively Skewed
the distribution's tail extends to the left, in a negative direction - occurs sometimes when there is a ceiling effect. mean<median<mode
