Transcript Chapter 14 PPT

Discrete Math
14.1
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Data Sets:
• Data set: collection of data values.
• Frequency: The number of times a data entry occurs.
• Bar Graph: Visual representation of the frequencies for
discrete data.
• Outliers: Data points that do not fit the overall pattern of
data.
• Relative Frequencies: Expressed as percentages of the
total population.
• Pictograms: Uses icons instead of bars.
Discrete Math
14.2
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Variables:
• Variable: Any characteristic that varies with the
members of a population.
• Quantitative data: numerical data.
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Continuous: Difference between data is small.
Discrete: Change between values by increments
• Qualitative: categorical variables described by
characteristics that cannot be measured
numerically. (eye color, freshmen...)
To be continued…
Discrete Math
14.2 (Continued...)
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Variables: (Continued...)
• Pie Chart: represents the entire population using
percentages.
• Class intervals: (rule: between 5 and 20) range of
breakup of scores.
• Histogram: Used when numerical value is continuous.
Bars are not spaced.
Discrete Math
14.3
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Measures of Location:
• Average: Sum / N
• Percentile: (p)th percentile such that p is the
percent of data that falls at or below this value
and the rest falls above.
• Locator (L): is the location of the data item (d)
at the given percentile.
To be continued…
How do you Find the Percentile?
 1.
Sort the data from smallest to largest
 2. Compute the locater using the
percentile given. L = p/100 x N
 3. If the locater is a decimal number ,
round up.
 4. If the locater is a whole number, take
the average.
Discrete Math
14.3 (Continued...)
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Median: the data item in the middle if N is
odd, or the average of the two middles if N
is even.
• Mode: Data item that occurs most often.
• First Quartile: 25th percentile or the median of
the first half of the data.
• Third Quartile: 75th percentile or the median of
the second half of the data.
To be continued…
Discrete Math
14.3 (Continued...)
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Numerical summaries (Continued...)
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Five Number Summary: min, max, Q1, Q3, median.
Box Plots: Based on five number summary
1. Find the 5 number summary
2. Draw the box from Q1 to Q3
3. Draw a line for the median inside the box.
4. Draw one whisker from the minimum to the box, and
one from the maximum to the box.
Discrete Math
14.4
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Spread:
• Range: difference in the max and min.
• Interquartile Range (IQR): difference in the first and
third quartile.
• Standard Deviation: Used to measure the spread or
variability.
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Find deviations from mean: data value - data mean
Square the deviations from mean: (X - X’)2
Find the average of the square deviations and this is
variance.
Standard Deviations (σ) is the square root of variance.
2
• σ = Σ (X - X’)
N
Discrete Math