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What is the mode?
The most commonly occurring value in the data set
What is the median?
- A value that divides the sample scores into two halves
- Equal numbers of scores lie above and below the median
How might one find the median for a data set?
- For an odd number of figures, take the middle value
- For an even number, take the middle two, add them and then divide the total by 2
How might one calculate the arithmetic mean?
Find the sum of all values and divide that figure by the number of values
What do Y values represent?
The scores for data sets
What does Y (bar) represent?
The mean of values in the data set
What does ∑ represent?
- The operation of addition
- (∑Y: add up all Y values)
How can the mean be said to be a balance point?
The sum of distances before the mean is equal to the sum of distances after it
If the variable is categorical, what is the most appropriate measure of central tendency?
If the distribution is normal (symmetrical with no outliers) what is the most appropriate measure of central tendency?
What effects does a positive skew have on measures of central tendency?
- The mode stays the same
- The median score increases (higher than the mode)
- The mean score increases (higher than the median)
What effects does a negative skew have on measures of central tendency?
- The mode stays the same (for the distribution of scores)
- The median score decreases (lower than the mode)
- The mean score decreases (lower than the median)
What are the relevant sensitivities of the mean?
- Sensitive to the exact values of all scores in the distribution
- Very sensitive to extreme scores (outliers)
- More sensitive than the median to outliers or legitimate data points that lie on the fringes
What are quartiles?
Divisions of data into quarters
What are the tree quartiles?
- Lower quartile: Divides the first 25% of the scores from the upper 75%
- Median: Divides the first 50% from the second half
- Upper quartile: Divides the fist 75% from the upper 25%
What is the range?
- The difference between the highest and lowest scores
- It is only based on two scores, however and is unstable and vulnerable to outliers
What is the interquartile range?
- The difference of the values of the third and first quartile
- Sometimes called the midrange as it it the range of the middle 50% of scores
What are the deviation scores?
The value of the Y scores minus the mean
What is the mean of deviation scores?
- This is because the scores always sum to 0
What are absolute deviations?
- The removal of minus signs from the deviation scores
- This is valid, but is rarely used
What is the variance?
- The degree of dispersion of results around the mean
- Each score is represented as a deviation and dispersion is measured in terms of the size of deviation
What is the sum of squares?
- The sum of the squared mean values
- SS= ∑[Y-Y(bar)](squared)
What is the variance?
- The sum of squares divided by the number of results -1
- n-1 is known as the degrees of freedom
What is the standard deviation in relation to variance?
The square root of the variance value
Why is the standard deviation better than the variance?
It is in the same units of measurements as the original score
What us the symbol for variance?
What is the symbol for standard deviation?