Chapter 2 Flashcards
What is a frequency table?
Shows discrete data, values, or scores, together with the frequency of each score
Why are frequency tables useful?
Organize and summarize raw data to show the spread or dispersion of data
What is frequency?
Tall of the number of observations in each category
What values does frequency include?
Every value between the highest and lowest score
What is a relative frequency distribution?
Number of scores in each interval represented as proportions or percentages
What is a cumulative frequency distribution?
Displays number of scores at or below each interval
What is a relative cumulative frequency distribution?
Displays proportion or % of scores that fall at or below each interval
What is step 1 in creating a grouped distribution?
Determine the range of the scores (highest score- lowest score)
What is step 2 in creating a grouped distribution?
Select and interval width (i)
What is step 3 in creating a grouped distribution?
Determine the score at which each interval should begin (this score should be divisible by the interval width)
What is step 4 in creating a grouped distribution?
Count up the number of observations in each interval
What do relative frequency distributions allow you to compare?
Distributions of different sizes
What are the advantages of grouped distributions?
Easier to understand and communicate
What are the disadvantages of grouped distributions?
Sacrifices some precision
What does a larger interval width mean?
More grouping error
What does our frequency distribution only show?
Apparent limits of our intervals
How do you find the real limits?
Look one half unit below the lowest value and one half unit above the highest value
How is half a unit determined?
Where the discrete measurement ends
What is the mode?
Most frequently occurring score
What is central tendency?
Single summary figure that describes the central location of a distribution
What is the median?
Score that evenly splits the distribution
What is the mean?
Sum of all scores/total number of the scores
What would be the best guess if you had to look at a single value for a person in a group?
Mode
What are the pros of the mode?
Easy, can be used with any scale of measurement
What are the cons of the mode?
Not all distributions have modes, some have multiple modes, and it has poor sampling stability
To determine the median what first must be done to the scores?
Rank order them
What are the pros of the median?
Greater sampling stability, not impacted by outlier scores
What are the cons of the median?
Only takes information from the center of a distribution
What does the sigma symbol mean? (E)
Sum of whatever follows
What does the X symbol mean?
Specifies a particular set of scores
What is the symbol of the mean for a population?
u
What does the symbol N mean?
Total number of scores in the interval/population
What does the symbol n mean?
Total number of scores in a sample
What is the mean sensitive to?
Each score in the distribution
What can you use central tendency to create?
Deviation scores
What is a deviation score?
Difference between each score and the central tendency (X - Mean)
What is the sum of deviations from the mean always?
ZERO
Which measure is the balance point of a distribution?
Mean
What happens if the distribution is symmetrical?
Mean, median, and mode are all the same
What direction will a positive distribution be leaning?
Left
What direction will a negative distribution be leaning?
Right
What can figures convey?
A lot of information quickly
When are figures a problem?
If the figure is not well constructed
Why do you have to label figures and graphs?
To know what they represent (also need a title)
What is variability not?
Information about an individual score, shape of a distribution
What type of chart do you always have to use relative frequencies for?
Pie
What should the y-axis of a distribution always start at?
Zero
What should you do if you are working with interval or ratio data?
The intersection of X and Y axes should be zero
What should you do if the intervals do not reach zero in your data?
Note this break on your graph
What are the figure types?
Histogram, frequency polygon, and Ogive Curve
What can the y-axis be?
Frequencies or relative frequencies
What are the boundaries of each bar?
The real limits of the intervals
What is the x-axis on a histogram?
Score intervals (labeled using the midpoint of interval)
What are histograms used for?
To represent interval and ratio data
When would you get a bimodal distribution?
Data from two underlying populations (two modes)
What is a percentile point?
Place on a measurement scale where a specified percentage of a distribution falls below
What is a percentile rank?
Percentage that corresponds to a specific point on measurement scale
What is variability?
Single statistic that best represents the degree of (dis)similarity between the scores
What does central tendency represent in regards to tables?
Location of scores
What do variability measures include?
Range, semi-interquartile range, variance, and standard deviation
What does the range increase with?
Sample size
What is a detail of the range?
Only two scores affect the value (highly unstable)
What is the semi-interquartile range (Q)?
Half the distance between the first and third quartiles
What is a quartile point?
Three score points that divide distributions into four parts with = number of frequencies in each part
What is the equation for Q?
Q= P75- P25/ 2
What are some details of the semi-interquartile range?
More stable than range, only sensitive to middle 50% of the distribution (like median)
What does the variance rely on?
Summing deviation scores
Why do we accomplish by squaring each deviation score?
We make them all positive
What do we do to get the standard deviation?
Take the square root of the variance
What are properties of S2 and S?
Sensitive to all scores, bad for describing distributions with outlets, good sampling stability, minimized around mean
When are squared deviations the smallest?
Around the mean
What are absolute deviations?
Minimized around the median
What is a z-score?
Distance of a score from the mean in standard deviation units
How do you get a z-score?
The deviation score divided by standard deviation of the distribution
What is the z score formula?
z= X-Mean/ Sx
What is the mean of any distribution in a z score?
Zero
What is the standard deviation of any distribution in z-scores?
One
What is unique about a z-score shape?
Shape of distribution is same as with the raw scores
What are the advantages of z-scores?
Consistent relationship between z-scores and raw scores unlike percentile ranks
What do standard scores allow?
Some comparisons across distributions of different sizes and scales (roughly the same shape)
When is a grouped frequency table useful?
Number of scores is so large that displaying them incrementally would make table to large to be a useful summary
A grouped frequency table is likely to have between 5 and
________ classes.
15
What is the midpoint?
Point between the upper and Lower class limits
What is a frequency polygon?
Form of a line graph that emphasizes continuous change in frequencies
What is a simple way to make a frequency polygon?
Basically plot the frequency and along the x-axis do the intervals and y-axis do frequencies
What type of data are histograms used for?
Numerical data in continuous categories
What type of data are bar charts used for?
Frequencies of categorical data
What type of chart should nominal data be put into?
Bar charts, pie charts
What types of charts should interval and ration be put into?
Histograms, ogive, and frequency polygons
What is an ogive?
Used to show how many data values lie below or above a particular value in a set
What is an easy way to make an ogive?
Plot cumulative frequencies but on the x-axis are the lower class limits and on the y-axis are the higher class limits
What does a dot plot show?
Frequencies of categories
What is a unimodal distribution?
Having one of the highest frequency or value
What is a bimodal distribution?
One with two equal high score frequencies, not considered bimodal unless almost equal
What is a multimodal distribution?
Has multiple equal peaks
What does a negative skew have?
Relatively few low values
What does a positive skew have?
Relatively few high values
What is the floor effect?
Scores pile up against some lower limit resulting in a positive skew
What is the ceiling effect?
Scores pile up against some upper limit resulting in a negative skew
What is the mean most sensitive to?
Outliers or extreme scores
What is S2
Sample variance
