14.114.1 Data Sets:Data Sets:

• Data set: collection of data values.Data set: collection of data values.• Frequency: The number of times a data entry occurs.Frequency: The number of times a data entry occurs.• Bar Graph: Visual representation of the frequencies for Bar Graph: Visual representation of the frequencies for

discrete data.discrete data.• Outliers: Data points that do not fit the overall pattern of Outliers: Data points that do not fit the overall pattern of

data.data.• Relative Frequencies: Expressed as percentages of the Relative Frequencies: Expressed as percentages of the

total population.total population.• Pictograms: Uses icons instead of bars.Pictograms: Uses icons instead of bars.

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14.214.2 Variables:Variables:

• Variable: Any characteristic that varies with the Variable: Any characteristic that varies with the members of a population.members of a population.

• Quantitative data: numerical data.Quantitative data: numerical data. Continuous: Difference between data is small.Continuous: Difference between data is small. Discrete: Change between values by incrementsDiscrete: Change between values by increments

• Qualitative: categorical variables described by Qualitative: categorical variables described by characteristics that cannot be measured characteristics that cannot be measured numerically. (eye color, freshmen...)numerically. (eye color, freshmen...)

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To be continued…

14.2 (Continued...)14.2 (Continued...) Variables: (Continued...)Variables: (Continued...)

• Pie Chart: represents the entire population using Pie Chart: represents the entire population using percentages.percentages.

• Class intervals: (rule: between 5 and 20) range of Class intervals: (rule: between 5 and 20) range of breakup of scores.breakup of scores.

• Histogram: Used when numerical value is continuous. Histogram: Used when numerical value is continuous. Bars are not spaced.Bars are not spaced.

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14.314.3 Measures of Location:Measures of Location:

• AverageAverage: Sum / N: Sum / N• PercentilePercentile: (p)th percentile such that p is the : (p)th percentile such that p is the

percent of data that falls at or below this value percent of data that falls at or below this value and the rest falls above.and the rest falls above.

• Locator (L): is the location of the data item (d) Locator (L): is the location of the data item (d) at the given percentile.at the given percentile.

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To be continued…

How do you Find the Percentile?How do you Find the Percentile?

1. Sort the data from smallest to largest1. Sort the data from smallest to largest 2. Compute the 2. Compute the locaterlocater using the using the

percentile given. L = p/100 x Npercentile given. L = p/100 x N 3. If the 3. If the locaterlocater is a decimal number , is a decimal number ,

round up.round up. 4. If the 4. If the locaterlocater is a whole number, take is a whole number, take

the average.the average.

14.3 (Continued...)14.3 (Continued...) MedianMedian: the data item in the middle if N is : the data item in the middle if N is

odd, or the average of the two middles if N odd, or the average of the two middles if N is even.is even.• ModeMode: Data item that occurs most often.: Data item that occurs most often.• First QuartileFirst Quartile: 25: 25thth percentile or the median of percentile or the median of

the first half of the data.the first half of the data.• Third QuartileThird Quartile: 75: 75thth percentile or the median of percentile or the median of

the second half of the data.the second half of the data.

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To be continued…

14.3 (Continued...)14.3 (Continued...) Numerical summaries (Continued...)Numerical summaries (Continued...)

• Five Number Summary: min, max, QFive Number Summary: min, max, Q11, Q, Q33, median., median.

• Box PlotsBox Plots: Based on five number summary: Based on five number summary• 1. Find the 5 number summary1. Find the 5 number summary

• 2. Draw the box from Q2. Draw the box from Q11 to Q to Q33

• 3. Draw a line for the median inside the box.3. Draw a line for the median inside the box.• 4. Draw one whisker from the minimum to the box, and 4. Draw one whisker from the minimum to the box, and

one from the maximum to the box.one from the maximum to the box.

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14.414.4 Spread:Spread:

• Range: difference in the max and min.Range: difference in the max and min.

• Interquartile Range (IQR): difference in the first and third Interquartile Range (IQR): difference in the first and third quartile.quartile.

• Standard Deviation: Used to measure the spread or Standard Deviation: Used to measure the spread or variability.variability.

Find deviations from mean: data value - data meanFind deviations from mean: data value - data mean Square the deviations from mean: (X - X’)Square the deviations from mean: (X - X’)22

Find the average of the square deviations and this is variance.Find the average of the square deviations and this is variance. Standard Deviations (σ) is the square root of variance.Standard Deviations (σ) is the square root of variance.

•

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σ = Σ (X - X’)2

N

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