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09 Midterm Review-1

# Line charts trend charts time series are effective

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Line Charts (trend charts, time series) are effective tools to represent data that are measured over time (e.g., monthly, quarterly, annually) A scatter diagram is a graphical presentation between two quantitative variables. 8

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Constructing a Stem and Leaf Diagram: Describing Data Graphically 9 the stem Each digit to the right vertical line 6 7 8 9 10 11 12 13 14 8 9 2 3 3 5 6 6 0 1 1 1 2 3 4 5 6 1 2 2 2 4 5 5 6 7 8 8 0 0 2 4 6 6 6 7 8 2 3 5 5 8 9 9 4 6 7 8 2 4 1
Describing Data Graphically - Summary 10 Categorical Data Tabular Methods Frequency distribution Relative frequency distribution Percent frequency distribution Graphical Methods Bar chart Pie chart Quantitative Data Tabular Methods Frequency distribution Relative frequency distribution Percent frequency distribution Cumulative frequency distribution Cumulative relative frequency distribution Cumulative percent frequency distribution Graphical Methods Histogram Ogive

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Measures of Center, Location, and Variation 11 Mean: Sum of values divided by the number of values Median: In an ordered array (lowest to highest), the median is the number that splits the distribution in half numerically Mode: The value that occurs most Shape of a distribution: Mean = Median Mean < Median Median < Mean Right-Skewed Left-Skewed Symmetric (Longer tail extends to left) (Longer tail extends to right)
Measures of Center, Location, and Variation 12 Percentiles Arrange the data in increasing order Compute the percentile index: If i is not an integer, round up. The next integer greater than i denotes the position of the p th percentile. If i is an integer, the p th percentile is the average of the values p = percentile of interest n = number of observations Quartiles split the data into four parts, with each part containing approximately one- fourth, or 25% of the observations. Q1: first quartile, or 25th percentile Q2: second quartile, or 50th percentile (also the median) Q3: third quartile, or 75th percentile

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Measures of Center, Location, and Variation 13 Box and Whisker Plot The center box extends from Q1 to Q3 The line within the box is the median The whiskers extend to the limits Outliers are plotted outside the calculated limits 25% 25% 25% 25% Outliers Lower 1st Median 3rd Upper Limit Quartile Quartile Limit * * The lower limit is Q1 – 1.5 (Q3 – Q1) The upper limit is Q3 + 1.5 (Q3 – Q1)
Measures of Center, Location, and Variation 14 Range Range = Largest value – Smallest value Ignores the way in which data are distributed Sensitive to outliers IQR is the difference between the third quartile and the first quartile; Q3 – Q1 Variance Population Variance Sample Variance Standard Deviation Population Standard Deviation Sample Standard Deviation Coefficient of Variation Shows variation relative to mean Standardized Data Values N μ) (x σ N 1 i 2 i 2 = - = 1 - n ) x (x s n 1 i 2 i 2 = - = N μ) (x

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Line Charts trend charts time series are effective tools to...

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