Chapter 3 Statistics

Front 1

arithmetic mean

Back 1

computed by adding all the values of the variable in the data set and dividing by the number of observations.

generally just referred to as the mean. It is sensitive to extreme values.

usually uses the symbol xbar

Front 2

population arithmetic mean

Back 2

(μ pronounced mew) is computed using all of the individuals in the population. It is a parameter.

Front 3

sample arithmetic mean (x with a bar over the top pronounced x-bar)

Back 3

is computed using sample data. The sample mean is static.

Front 4

median

Back 4

the value that lies in the middle of the data when the the data is arranged in ascending order. We use M to represent the median. Median is resistive to extreme values.

to help remember think of the median of the road. It divides the road in half.

Front 5

distribution shape in relation to mean and median

Back 5

skewed left mean smaller than median

Front 6

mode

Back 6

a variable is the most frequent observation of the variable that occurs in the data set. Use this when the data are qualitative or the most frequent observation is needed.

Front 7

range

Back 7

the difference between the largest and the smaller data value. range is not resistant to change and it does not consider all of the data values.

Front 8

standard deviation is based on

Back 8

the deviation from the mean

Front 9

population standard deviation

Back 9

of a variable is the square root of the sum of squared deviations about the population mean divided by the number of observations in the population, N. That is, it is the square root of the mean of the squared deviations about the population mean. The population standard deviation is usually lower case greek sigma, σ

N is the number of observations
μ is the population

Front 10

conceptual formula

Back 10

because it allow us to see how standard deviation measures are spread

Front 11

sample standard deviation, s

Back 11

s of a variable is the square root of the sum of squared deviations about the sample mean divided by n-1 where n is the sample size.

standard deviation is not resistant

Front 12

deviation about the mean

Back 12

the ith observation is xi- u

For a sample, the deviation about the mean for the ith observation is xi - xbar

Front 13

computational formula

Back 13

σ =√ ∑x²i - [ (∑xi)² / N ] ÷ N

where ∑x²i means to square each observation and then sum these squared values and
(∑xi)² means to add up all the observations and square the sum.

Front 14

degrees of freedom

Back 14

n-1 because from the first n-1 observation have freedom to be whatever value they wish, but the nth value has no freedom. It must be whatever value forces the sum of the deviations about the mean to equal zero.

Front 15

the larger the standard deviation

Back 15

the more dispersion the distribution has (when comparing 2 populations.)

Front 16

variance

Back 16

the variance of a variable is the square of the standard deviation.

Front 17

The population variance is

Back 17

σ²

Front 18

the sample variance is

Back 18

s²

Front 19

z-score

Back 19

represents the distance that a data value is from mean in terms of standard deviations.

we find it by subtracting the mean from the data value and dividing this result by the standard deviation. There is both a population z-score and a sample z-score

The z score is unitless It has a mean of 0 and a standard deviation of 1. it allows us to compare apples to oranges.

Front 20

kth percentile

Back 20

denoted Pk of a set of data is a value such that k percent of the observations are less than or equal to the value.

Front 21

quartiles are

Back 21

resistant to extreme values

Front 22

interquartile range IQR

Back 22

the range of the middle 50% of the observations in the data set. That is, the IQR is the difference between the third and first quartiles and is found using the formulate IQR= Q3 - Q1

Front 23

outlier

Back 23

If a data value is less than the lower fence or greater than the upper fence, it is considered an outlier.