More Graphs and Displays. Stem-and-Leaf Plots Each number is separated into a STEM and LEAF component. The STEM is the leftmost digit(s). The LEAF is.

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Presentation transcript:

More Graphs and Displays

Stem-and-Leaf Plots Each number is separated into a STEM and LEAF component. The STEM is the leftmost digit(s). The LEAF is the rightmost digit. It’s important to include a key to identify values. For example… Key: 15 | 5 = 155

Use the stem-and-leaf plot to list the actual data entries.

Make a stem-and-leaf plot: Ages of the top 30 highest paid CEOs (Forbes Magazine)

Pie Chart (for Qualitative Data) A circle divided into sectors that represent categories. The area of each sector is proportional to the frequency of the category.

Pareto Chart (for Qualitative Data) Vertical bar graph in which the height of each bar represents the frequency or relative frequency. Bars are positioned in order of decreasing height, left to right. EX: Make a Pareto chart Ultraviolet indices for 5 cities at noon: AtlantaBoiseConcordDenverMiami

Scatter Plot (for Paired Data Sets) Paired data  Ordered pairs. Plot on a coordinate plane. Independent variable on the x-axis.

EX: make a scatter plot: # of students per teacher Avg teacher’s salary (in thousands$)

Measures of Central Tendency

Measure of Central Tendency: A value that represents a typical, or central, entry of a data set. 3 most common are MEAN, MEDIAN, and MODE

MEAN: sum of the data entries divided by n

MEDIAN The data entry in the MIDDLE. List data from least to greatest. Find the middle value. (For even n, find the average of the 2 middle values)

MODE Data entry that occurs MOST often (highest frequency) A data set may have no mode or have more than mode. BIMODAL = 2 modes.

EX: Find mean, median, and mode for the data set. The tuition and fees (in thousands of dollars) for the top 14 universities:

Weighted MEAN: data values have different weights.

EX: find the weighted mean The scores and their percents of the final grade for an archaeology student are shown. What is the student’s mean score: SCOREPercent of Final Grade Article Reviews9510% Quizzes10010% Midterm Exam8930% Student Lecture10010% Final Exam9240%

Ex: find the weighted mean The mean scores for students in a statistics course (by major) are shown below. What is the mean score for the class? 9 engineering majors: 85 5 math majors: business majors: 81

Mean of a Frequency Distribution

EX: Find the mean The city mileage (in miles per gallon) for 24 family sedans: Mileage (in mpg)Frequency

Shapes of Distributions Distributions may look.. Symmetric Uniform Skewed Left Skewed Right

Symmetric

Uniform

Skewed Left

Skewed Right