Flashcards in Test 2: Ch 4-6 Deck (31):
Measures of Central Tendency
Categories or scores that describe what is average or typical of the distribution.
The category/score with the highest frequency (or %)
Three factors for choosing appropriate MOCT
1. The way the variables are measured.
2. The shape of the distribution.
3. The purpose of the research.
Two scores or categories with the highest frequency
The score that divides the distribution into two equal parts so that half the cases are above it and half are below it.
Finding median for odd variable
A score below which a specific percentage of the distribution falls.
A measure of central tendency that is obtained by adding up all the scores and dividing by the total number of scores. It is the arithmetic average.
Raw scores of the variable Y
The mean of Y
The sum of all the Y scores
The number of observations/cases
Finding the mean in a frequency distribution
Y= (sigma)f (Y)/N
The frequencies at the right and left tails of the distribution are identical; each half of the distribution is the mirror image of the other.
A distribution with a few extreme values on one side of the distribution.
*mean, median and mode do NOT coincide. The mean falls closest to the tail of the distribution where a small number of extreme scores are located
Positively skewed distribution
A distribution with a few extremely high values.
Negatively skewed distribution
A distribution with a few extremely low values
Identifying shape of distribution
1. In unimodal distributions, when the mode, median, and mean coincide or are almost identical, the distribution is SYMMETRICAL.
2. When the mean is higher (or to the right) than the median, the distribution is POSITIVELY SKEWED.
3. When the mean is lower (or to the left) than the median, the distribution is NEGATIVELY SKEWED.
Highest score - lowest score
Median for even
-Arrange from least to greatest
-find mean of two middles
Measures of variability
Numbers that describe diversity or variability in the distribution of a variable
Importance of measuring variability
Helps characterize and compare groups without prejudice
Index of qualitative variation (IQV)
A measure of variability for nominal variables.
Based on the ratio of the total number of differences in the distribution to the maximum number of possible differences within the same distribution.
1. Construct a percentagedistribution
2. Square the % for each category
3. Sum the squared %s
4. Calculate the IQV using the formula
Interquartile range IQR
The width of the middle 50% of the distribution.
The difference between lower (Q1) and upper (Q3) quartiles.
1. Draw a box between the lower and upper quartiles
2. Draw a solid line within the box to mark the median
3. Draw vertical lines outside the box, extending to the lowest and highest values
Box Plot: symmetrical distribution
Box is in the center of the range and the median is in the center of the box.
Box plot: skewed distribution
Box and/or median are not centered.
Closer to Q1 when more cases have lower scores, closer to Q3 when more cases have higher scores.
The average of the squared deviations from the center/mean of the distribution