14.1 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 discrete data.Bar Graph: Visual representation of the frequencies for discrete data. Outliers: Data points that do not fit the overall pattern of data.Outliers: Data points that do not fit the overall pattern of data. Relative Frequencies: Expressed as percentages of the total population.Relative Frequencies: Expressed as percentages of the total population. Pictograms: Uses icons instead of bars.Pictograms: Uses icons instead of bars. Discrete Math

14.2 Variables: Variables: Variable: Any characteristic that varies with the members of a population.Variable: Any characteristic that varies with the 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 increments Discrete: Change between values by increments Qualitative: categorical variables described by characteristics that cannot be measured numerically. (eye color, freshmen...)Qualitative: categorical variables described by characteristics that cannot be measured numerically. (eye color, freshmen...) Discrete Math To be continued…

14.2 (Continued...) Variables: (Continued...) Variables: (Continued...) Pie Chart: represents the entire population using percentages.Pie Chart: represents the entire population using percentages. Class intervals: (rule: between 5 and 20) range of breakup of scores.Class intervals: (rule: between 5 and 20) range of breakup of scores. Histogram: Used when numerical value is continuous. Bars are not spaced.Histogram: Used when numerical value is continuous. Bars are not spaced. Discrete Math

14.3 Measures of Location: Measures of Location: Average: Sum / NAverage: 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.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.Locator (L): is the location of the data item (d) at the given percentile. Discrete Math 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.

14.3 (Continued...) Median: the data item in the middle if N is odd, or the average of the two middles if N is even. 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.Mode: Data item that occurs most often. First Quartile: 25 th percentile or the median of the first half of the data.First Quartile: 25 th percentile or the median of the first half of the data. Third Quartile: 75 th percentile or the median of the second half of the data.Third Quartile: 75 th percentile or the median of the second half of the data. Discrete Math To be continued…

14.3 (Continued...) Numerical summaries (Continued...) Numerical summaries (Continued...) Five Number Summary: min, max, Q 1, Q 3, median.Five Number Summary: min, max, Q 1, Q 3, median. Box Plots: Based on five number summaryBox Plots: Based on five number summary 1. Find the 5 number summary1. Find the 5 number summary 2. Draw the box from Q 1 to Q 32. Draw the box from Q 1 to Q 3 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 one from the maximum to the box.4. Draw one whisker from the minimum to the box, and one from the maximum to the box. Discrete Math

14.4 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 quartile.Interquartile Range (IQR): difference in the first and third quartile. Standard Deviation: Used to measure the spread or variability.Standard Deviation: Used to measure the spread or variability. Find deviations from mean: data value - data mean Find deviations from mean: data value - data mean Square the deviations from mean: (X - X’) 2 Square the deviations from mean: (X - X’) 2 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. Discrete Math σ = Σ (X - X’) 2 N

Discrete Math