Averages and Measures of Spread Flashcards
(23 cards)
What do averages tell us?
Answer everyday questions and subject specific questions
What is the mean?
Add together all values and divide by the number of subjects
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X = mean
sum of x/ n
What is the median?
The middle observation in an ordered data set
(n+1)/2 th position
Add the 2 numbers either side of the position and divide by 2
What is the mode?
The number that appears most frequently
What is the problem with averages?
An extreme value can really influence some measures of average
What is normal distribution?
The mean and the median are approximately equal
What is positively skewed?
The mean will be greater than the median
What is negatively skewed?
The mean will be less than the median
What are the different types of variables?
Ratio, interval, ordinal and nominal
On SPSS - Nominal, ordinal and scale
Continuous and categorical
Outline categorical and continuous variables
Continuous and ordinal categorical variables you calculate a mean or median, all ratio/interval and many ordinal
Categorical (nominal) - No sense to calculate a mean or median
What is a factor?
A categorical variable
How do we decide on the best analysis?
Think of the type of variables
Are the variables continuous or categorical if both then use a contingency table
If you have a grouping variable and a continuous variable then compare means or medians
What is a percentile?
A value at or below which a specified percentage of the scores in a distribution fall
Allows us to say where a value lies on a distribution of data
How do we calculate percentiles?
Value of a percentile = [Percentile/100] x (n + 1)th observation
What are quartiles?
Lower quartile is the 25th percentile
Median is the 50th percentile
Upper quartile is the 75th percentile
What are quintiles, deciles and tertiles ?
Quintiles are split into 20%
Deciles are split into 10%
Tertiles are split into thirds
What is spread?
Indicator of the distribution of the data
What are the 4 measures of spread?
Range - The difference between the highest and lowest value
Interquartile range - the difference between the upper and lower quartile (for skewed data)
Standard deviation - measures the average deviation from the mean
Variance - Standard deviation squared (not used as much as not the same scale as original variable)
Outline box plots
Biggest and smallest observations
Median
Lower quartile
Upper quartile
Interquartile range
Lower fence - LQ - (1.5 x IQR)
Upper fence - UQ + (1.5 x IQR)
What is the difference between high and low resolution ordinal data?
High resolution had enough values to calculate a median or create a boxplot
When do we use SD?
When the data is not significantly skewed
Predominantly continuous data
How do we calculate SD?
Residual - difference between a particular observation (y) and the mean
The SD is the square root of the sum of the squared residuals over n -1
How do we interpret SD?
A larger SD means the data are more spread out
Smaller SD means the data is closer together
