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mccannell_stats_02
Vocabulary for chapter 2 of Elementary Statistics (Larson and Farber)
29
Mathematics
11th Grade
04/29/2011

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Term
class
Definition

A class is a category or range of data values. We usually divide a data set into a number of classes to help us detect patterns in the data.

 

The number of  classes should be between 5 and 20 to make it easier to detect patterns. Use one of the following formulae to guide your selection of a number of classes to use:

 

for relatively small data sets: classes = √n

 

for large data sets: classes = 1 + 3.3log(n)

Term
class width
Definition

Class width is the distance from the lower limit (starting value) of one class to the lower limit of the next class.

 

class width = range/number of classes

 

You must round up to ensure you include all data values. With integer (whole number) data, you must round to the next whole number if this formula yields a whole number.

Term
frequency
Definition

The frequency f of a class is the number of data entries in the class.

Term
relative frequency
Definition

The relative frequency of a class is the class frequency divided by the sample size. (You may express it as a non-percent decimal ".355" or as a percentage "35.5%."

 

relative frequency = f/n

Term
frequency distribution
Definition

A frequency distribution is a table with one column for the classes into which a data set has been divided and another column for the frequency of each class.

Term
frequency histogram
Definition

A frequency histogram is a bar graph that represents the frequency distribution of a data set. A histogram has the following properties:

  1. The horizontal scale (x-axis) is quantitative and measures the data values.
  2. The vertical scale (y-axis) measures the frequency of the classes.
  3. Consecutive bars must touch.
Term
cumulative frequency
Definition

The cumulative frequency for a class is the sum of the frequency for that class and the frequencies of all previous classes.

Term
measure of central tendancy
Definition

A measure of central tendancy is a value that represents a typical, or central, entry of a data set.

 

The mean, median and mode of a data set are measures of central tendancy.

Term
mean
Definition

The mean of a data set is the sum of the data entries divided by the number of entries. The mean is not resistant to outlying values.

 

population mean: μ=Σx/N


sample mean: x bar = Σx/n

Term
median
Definition

The median of a data set is the value that lies in the middle of the data when the data set is ordered.

 

The median is resistant to outlying values.

Term
mode
Definition

The mode of a data set is the data entry that occurs with the greatest frequency. If no data entry is repeated, the data set has no mode. If two entries occur with the same greatest frequency, each entry is a mode and the data set is called bimodal.

 

For qualitative data, mode is the only measure of central tendancy.

Term
symmetric
Definition

A frequency distribution is symmetric when a vertical line can be drawn through the middle of a graph of the distribution and the resulting halves are approximately mirror images.

Term
uniform
Definition

A frequency distribution is uniform when all entries, or classes, in the distribution have equal or approximately equal frequencies. A uniform distribution is also symmetric.

Term
skewed
Definition

A frequency distribution is skewed if the "tail" of the graph elongates more to one side than to the other.

 

A distribution is skewed left (negatively skewed) if the tail extends to the left. A distribution is skewed right (positively skewed) if the tail extends to the right.

Term
measure of variation
Definition

 A measure of variation is a numerical description of how "spread out" a data set is.

 

Range, variance and standard deviation are measures of variation.

Term
range
Definition

The range of a data set is the difference between the maximum and minimum data entries in the set.

 

range = (maximum entry) – (minimum entry)

Term
deviation
Definition

the deviation of an entry x in a data set is the difference between the entry and the mean of the data set.

 

population: deviation of x = x – μ

 

sample: deviation of x = xx bar

Term
squared devation (expression)
Definition

 

population: (x – μ)2

 

sample: (xx bar)2

Term
sum of squared deviations (expression)
Definition

population: Σ(x – μ)2

 

sample: Σ(xx bar)2

Term
variance (equations)
Definition

population: σ2 = Σ(x – μ)2/N

 

sample: s2 = Σ(xx bar)2/(n-1)

Term
standard deviation (equations)
Definition

population: σ = √(Σ(x – μ)2/N)

 

sample: s = (Σ(xx bar)2/(n-1))

Term
measure of position
Definition

A measure of position specifies where in a data set an entry is located.

 

Quartiles, percentiles ans z-scores are measures of position.

Term
five-number summary
Definition

The five-number summary of a data set refers to the minimum entry, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum entry.

Term
minimum
Definition

The minimum is the smallest value in a data set.

Term
maximum
Definition

The maximum is the largest value in a data set.

Term
quartile
Definition

A quartile is one of three numbers (the first, second and third quartiles, Q1, Q2 and Q3) that divide a data set into four approximately equal parts. 75% of the values in a data set fall below the third quartile.

Term
percentile
Definition

A percentile is one of 99 numbers (P1 to P99) that divide a data set in 100 roughly equal parts. 99% of the data values fall below the 99th percentile.

Term
interquartile range
Definition

The interquartile range (IQR) is the difference between the third and first quartiles.

 

IQR = Q3 – Q1

Term
z-score (or standard score)
Definition

The z-score represents the number of standard deviations a given value falls from the mean.

 

z = (x – μ)/σ

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