cogs 10A final exam lec. 15 study guide

variability

quantitative measure of the degree to which scores are spread out from the mean (high variability), or clustered together toward the mean (low variability)

range

the difference between the largest score in the distribution (X max) and the lowest score in the distribution (X min)

exclusive range

most common measure of range that is computed by excluding one of the endpoints of a distribution, thus it is just the difference between a high or highest score and the low or lowest score

inclusive range

way of computing range that takes into account both endpoints that, rather than just computing the difference between the highest and lowest value, also computes the number of values included between highest and lowest values; (X max - X min) + 1

when is inclusive range useful

when dealing with discrete values and the data suggests the number of values should be emphasized

should type of range be specified?

yes, when using inclusive range it should be specified as “inclusive”, otherwise just saying “range” implies/assumes it is “exclusive”

advantage of range

simple to calculate and easy to calculate

disadvantage of range

Completely determined by the two extreme values and ignores every other score in the distribution; it often fails to give an accurate measure of variability for the entire distribution

quartiles

divide a distribution into four equal sections and are used to compute interquartile and semi-interquartile ranges

first quartile

separates the first 25% of the distribution from the rest of it; is found by computing the median of the lower half (lower 50%) of the distribution below the second quartile

second quartile

has 50% of the distribution above it, and 50% below it; computed by finding the median of the entire distribution

what measure of central tendency is equivalent to the second quartile?

median

third quartile

has 75% of the distribution below it; found by computing the median of the upper half (upper 50%) of the distribution past the second quartile

interquartile range

range between the third and first quartile; found by computing Q3 - Q1

semi-interquartile range

one-half of the interquartile range that provides a “typical” distance of scores from the median (Q2); found by computing (Q3 - Q1) / 2

semi-interquartile range and variability

the greater the range, the greater distance between scores from the mean, meaning there is more variability, and vice versa

advantage of semi-interquartile range

because it focuses on the middle 50% of a distribution, it is unlikely to be affected by extreme scores, making it a more reliable and stable measure of variability

disadvantage of semi-interquartile range

Doesn't take into account actual distances between individual scores, so it doesn't give a complete picture of how scattered/clustered score are

box plot

aka box-and-whisker plot; generated via the use of quartiles and represent median, quartiles, and range in one display

hinges

values that consist of the first and third quartiles that also make up/determine the box of the box plot,

“box” of box-plot

determined by its first and third quartile hinges; designates the middle 50% of scores and interquartile range

H-spread

aka the interquartile range; the distance between the box’s two hinges (Q1 and Q3)

inner fence

a point in the graph of a box plot that falls 1.5 times the H-spread above or below the appropriate hinge

computing lower fence

Q1 - (1.5 * H-spread)

computing upper fence

Q3 + (1.5 * H-spread)

adjacent values

values in the data of a box-plot graph/distribution that are no farther from the median than the inner fences

box plot whiskers

lines that are drawn from hinges out through the adjacent values extending through each last adjacent value on each side of the box

what does the vertical line drawn inside of the box represent

it represents the 2nd quartile/median

outliers (box plot)

any value more extreme than the end of the whiskers (more extreme than adjacent values) and thus are non-adjacent values since they fall outside of the inner fences; are plotted as individual points

what could outliers represent

COULD represent an error in measurement, in data recording/entry ,or it could be a legitimate value that just happens to be extreme