Stat 311 - Chapter 3

Front 1

mean

Back 1

average of a data set

best used when there are no skewed numbers

Front 2

median

Back 2

value that falls in the middle of the data when put in order from lowest to highest

best use when there are skewed numbers

Front 3

mode

Back 3

most common number of a data set

Front 4

standard deviation and variance

Back 4

std. dev. = √(variance)

variance = ∑ [(x - x_bar)²]/(n-1)

Front 5

right-skew graph of data
(where are measures of center?)

Back 5

parabolic graph with "tail" towards the right end;

mode is at peak of parabola; median is just to the right of mode;
mean is just to the right of median

Front 6

left-skew graph of data
(where are measures of center?)

Back 6

parabolic graph with "tail" towards the left end;

mode is at peak of parabola; median is just to the left of mode;
mean is just to the left of median

Front 7

symmetric graph of data
(where are measures of center?)

Back 7

mode, median, and mean are all at the peak of the parabola

Front 8

population symbols
(for mean, variance, std. dev)

Back 8

mean: μ
variance: σ²
std. dev.: σ

Front 9

range

Back 9

the lowest data point subtracted from the highest data point

Front 10

sample symbols
(for mean, variance, std. dev)

Back 10

mean: x_bar
variance: s²
std. dev.: s

Front 11

approximating std. dev.

Back 11

(range)/4

Front 12

z-score

Back 12

used to compare individuals from different populations

sample*: (x-x_bar)/s
population: (x-μ)/σ

*most likely only one we'll use

Front 13

midrange

Back 13

(min+max)/2... NOT (range)/2

Front 14

empirical rule

Back 14

for data sets having a distribution that is approximately bell shaped, the following properties apply:

1) about 68% of the individuals fall within 1 std dev of the mean
2) about 95% of all values fall within 2 std dev of the mean
3) about 99.7% of all values fall within 3 std dev of the mean

Front 15

usual and unusual

Back 15

if a data value falls within 2 std devs of mean, it is usual; if it does not, it is unusual

Front 16

percentile of value x

Back 16

(number of values < x)/(total number of values)

Front 17

5-number summary

Back 17

contains min, 25th percentile, median, 75th percentile, and max

Front 18

interquartile range (IQR)

Back 18

75th percentile - 25th percentile

Front 19

calculating outliers

Back 19

an outlier falls either:
> 75th %tile + (1.5)(IQR)
< 25th %tile - (1.5)(IQR)