Stats Chapter 2
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- •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
- numbers that separate classes without forming gaps between them..
- 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
- vertical scale measures the relative frequencies, not
Measure of central tendency
- •A value
- that represents a typical, or central, entry of a data set.
- common measures of central tendency:
- •The sum of all the data
- entries divided by the number of entries.
- notation: Σx = add all of the data
- entries (x) in the data set.
- •Population mean: u=Ex/N
- •Sample mean:x=Ex/n
- •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.
- number of entries: median is the mean of the two middle data entries.
- •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).
- difference between the maximum and minimum data entries in the set.
- •The data
- must be quantitative.
- •Range =
- (Max. data entry) – (Min. data entry)
- difference between the data entry, x, and the mean of the data set.
- data set:
- of x = x – μ
- data set:
- of x = x – x
- are numbers that partition (divide) an
- ordered data set into equal parts.
- approximately divide an ordered data
- set into four equal parts.
Interquartile Range (IQR)
- difference between the third and first quartiles.
- •IQR = Q3 – Q1
Standard Score (z-score)
- the number of standard deviations a given value x falls from the mean μ.
- 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
- 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.
population mean, µ, is
u = x1 + x2 + xn/N
the sample mean, x , is
x = x1 + x2 + xn/n
- 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.
- The sample variance is
- computed by determining the sum of squared deviations about the sample mean and
- then dividing this result by n – 1.
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