A bar graph wherein the bars touch each other; the heights of the bars correspond to the frequency values
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What does the the horizontal scale represent on histograms?
Classes of quantitative data values
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What does the the vertical scale represent on histograms?
Frequencies
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Relative Frequency Histogram
A graph with the same shape and horizontal scale as a histogram but the vertical scale is marked with relative frequencies
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Two types of misleading graphs
Nonzero axis and pictographs
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Median
The middle value when the original data values are arranged in order of increasing (or decreasing) magnitude
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If the number of data values is odd, the median is ___
the number located in the exact middle of the list
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If the number of data values is even, the median is ___
found by computing the mean of the two middle numbers
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Percentiles (Pk)
A value in a set of data such that k percent of the observations are less than or equal to the value
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Percentile of x (Px)=
number of values less than x/total number of values x 100
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Percentiles are used to give the ___
relative standing of an observation
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Quartiles
Divides the data set into fourths
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Q1
Denotates the 25th percentile
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Q2
Denotates the 50th percentile
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Q3
Denotates the 75th percentile
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The interquartile range (IQR)
The difference between Q3 and Q1; describes the variability of the middle 50% of the data values
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5-number summary
A subset of the data that consists of the minimum value, the first quartile, the median, the third quartile, and the maximum value
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Boxplots/box-and-whisker plots are constructed from ___
5-number summary
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What do boxplots show?
How far extreme values are from the bulk of the data
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Strengths of boxplots
Give a direct look at location and spread, identifies outliers, is great for comparing
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Weaknesses of boxplots
Symmetry and skewness can be judged but shape cannot
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Outlier
A data point that is not consistent with the bulk of the data from that group
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Measure of center
A value at the center or middle of a data set such as the mean, median, mode, or midrange
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Mode
The value that occurs with the greatest frequency in a data set
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Bimodal
When two data values occur with the same frequency
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Multimodal
When more than two values occur with the same frequency
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Arithmetic Mean
The average value of a data set found by adding the data values and dividing the total by the number of data values
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∑
The sum of a set of data values
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x
The variable usually used to represent the individual data values
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n
The number of data values in a sample (sample size)
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N
The number of data values in a population (population size)
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x̄= ∑x/n
The mean of a set of sample values (sample mean)
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μ = ∑x/N
The mean of all values in a population (population mean)
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Resistant
If extreme values (very large or very small) relative to the data do not affect its value substantially, then, the data is said to be resistant
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Bell-shaped Distribution
The highest frequency occurs in the middle and frequencies tail off to the left and the right of the middle
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Right Skewed
The tail extends to the right of the peak longer than to the left
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Left Skewed
The tail extends to the left of the peak longer than to the right
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Variation
the degree to which data are spread out
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Range (R)
The difference between the maximum and minimum data value
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Standard Deviation
A measure of the spread of the data
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Population Standard Deviation equation
[See slideshow]
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Sample Standard Deviation
[See slideshow]
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The standard deviation is a measure of ___
how much data values deviate from the mean
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The values of standard deviation can never be what?
Negative
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If all the values are exactly the same, what is the standard deviation?
Zero
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Larger values of standard deviation indicates what?
greater amounts of variation
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What can drastically change the value of the standard deviation?
Outliers
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Variance
Deviation about the mean; square of the standard deviation
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Population variance
Sum of the squared deviations about the population mean divided by the number of observations in the population
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Population variance equation
[See slideshow]
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Sample variance equation
[See slideshow]
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Sample variance
The sum of the squared deviations about the sample mean and divided by n-1
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z Score
The number of standard deviations that a given value x is above or below the mean. The z-score is unitless, it has a mean of 0 and a standard deviation of 1.
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