Stats Chapter 2
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Frequency Distribution
 •A table
 that shows classes or intervals of data with a count of the number of
 entries in each class.
 •The frequency, f, of a
 class is the number of data entries in the class.

Midpoint of a class
Lower class limit + Upper class limit divided by 2

Class boundaries
 •The
 numbers that separate classes without forming gaps between them..
 •The
 distance from the upper limit of the first class to the lower limit of the
 second class is 19 – 18 = 1.
 • Half
 this distance is 0.5.


Relative Frequency Histogram
 •Has the
 same shape and the same horizontal scale as the corresponding frequency
 histogram.
 •The
 vertical scale measures the relative frequencies, not
 frequencies.

Measure of central tendency
 •A value
 that represents a typical, or central, entry of a data set.
 •Most
 common measures of central tendency:
 §Mean
 §Median
 §Mode

Mean (average)
 •The sum of all the data
 entries divided by the number of entries.
 •Sigma
 notation: Σx = add all of the data
 entries (x) in the data set.
 •Population mean: u=Ex/N
 •Sample mean:x=Ex/n

Median
 •The value that lies in the
 middle of the data when the data set is ordered.
 •Measures the center of an
 ordered data set by dividing it into two equal parts.
 •If the data set has an
 §odd number
 of entries: median is the middle data entry.
 §even
 number of entries: median is the mean of the two middle data entries.

Mode
 •The data entry that occurs
 with the greatest frequency.
 •If no entry is repeated the
 data set has no mode.
 •If two entries occur with
 the same greatest frequency, each entry is a mode (bimodal).

Range
 •The
 difference between the maximum and minimum data entries in the set.
 •The data
 must be quantitative.
 •Range =
 (Max. data entry) – (Min. data entry)

Deviation
 •The
 difference between the data entry, x, and the mean of the data set.
 •Population
 data set:
 §Deviation
 of x = x – μ
 •Sample
 data set:
 §Deviation
 of x = x – x

Fractiles
 are numbers that partition (divide) an
 ordered data set into equal parts.

Quartiles
 approximately divide an ordered data
 set into four equal parts.

Interquartile Range (IQR)
 •The
 difference between the third and first quartiles.
 •IQR = Q3 – Q1

Standard Score (zscore)
 •Represents
 the number of standard deviations a given value x falls from the mean μ.

arithmetic mean
 The arithmetic mean of a
 variable is computed by determining the sum of all the values of the variable
 in the data set divided by the number of observations.

population arithmetic mean
 The population arithmetic mean is
 computed using all the individuals in a
 population.
 The population mean is a parameter.
 The population arithmetic mean is denoted by u .

sample arithmetic mean
 The sample arithmetic mean is
 computed using sample data.
 The sample mean is a statistic.
 The sample arithmetic mean is denoted by x.

the
population mean, µ, is
u = x1 + x2 + xn/N

the sample mean, x , is
x = x1 + x2 + xn/n

resistant
 A numerical summary of data is said to be resistant if extreme values (very large or small) relative to the
 data do not affect its value substantially.

sample variance
 The sample variance is
 computed by determining the sum of squared deviations about the sample mean and
 then dividing this result by n – 1.
