8.1 Types of Data Displays Remember to Silence Your Cell Phone and Put It In Your Bag!

Introduction Statistics Descriptive Statistics Inferential Statistics

Graphical Displays of Data Make the display user friendly Title Labels Scale  Use a uniform scale  When necessary use a broken line to indicate a jump in the scale Technology Pencil and paper Calculator Computer Software

Representing Frequency and Distribution of Data Frequency Table A table that organizes the data by recording the number of times a number (score) occurs in a set of data To make a frequency table: 1. Decide on the categories or intervals to use. When making a grouped frequency table, use intervals of equal length 2. Record the data by placing a tally mark for each score. 3. Count the number of tallies and write the number in the frequency column.

Age of Students City Track Meet Age of Students TallyFrequency 8||2 9|||3 10|||| |6 11||||4 12|||3 13|||| |6 14|||| |6

Frequency Table (cont.) Adv  Quick way to organize the data to get a picture of it  Makes it easy to identify numbers that occur several times  Easy to read and interpret Dis  When using grouped intervals some of the specific data may be lost

Representing Frequency and Distribution of Data Dot Plot A graphical display of the data using a horizontal number line To make a dot plot: 1. Draw a horizontal number line with scale markings for the range of the data. 2. Place a dot, circle, or × above the corresponding number line value.

Dot Plot (cont.) Adv  Quick way to organize the data to get a picture of it  Easy to spot the extremes of the data set and to note both outliers and clusters of points  Can see the actual data values Dis  Not practical for large data sets

Representing Frequency and Distribution of Data Stem and Leaf Plot (Ordered) A display of the data in a vertical format grouping scores with the same leading digits Use a legend To make a stem and leaf plot: 1. Decide on the number of digits in the data to be listed under the stems. 2. List the stems in a column from smallest to largest (or largest to smallest). 3. List the remaining digits in each data entry as leaves, smallest to largest (or largest to smallest).

Stem and Leaf Plot (cont.) Adv  Can see the actual data values  Makes it easy to identify numbers that occur several times Dis  Can be confusing to read  Not all data lends itself to this type of grouping

Representing Variation and Comparing Data Pictograph A graph which uses icons or figures to represent data values Use a legend to indicate what the icon represents May use fractions of an icon To make a pictograph: 1. Select categories or intervals for the data. 2. Choose an icon and decide what it represents. 3. Draw the appropriate number of icons for each category.

Pictograph (cont.) Adv  Uses a visual to show differences in numerical values Dis  May force the reader to make estimates of the data

Representing Variation and Comparing Data Histograph (or histogram) A graph which uses rectangles to display the frequency of a grouped data set To make a histograph: 1. Decide on the intervals to use. Set this up on the horizontal axis. 2. Find the frequency of each interval. Set this up on the vertical axis. 3. Draw rectangles that touch each other on the horizontal axis and have a height that represents the frequency of the interval.

Histograph (cont.) Adv  Can show gaps and clusters in the data  Traditional format many are used to reading Dis  Usually takes more time to construct than other graphic displays  Specific data may be lost  May force the reader to make estimates of the data

Representing Variation and Comparing Data Bar Graph A graph which uses rectangles to display a set of discrete data To make a bar graph: 1. Decide on the categories to use for each axis. 2. Draw equally spaced rectangles on the horizontal axis with heights that represent the related category.

Bar Graphs (cont.) Adv  Can show gaps and clusters in the data  Traditional format many are used to reading Dis  Usually takes more time to construct than other graphic displays  Specific data may be lost  May force the reader to make estimates of the data

Representing Part-to-Whole Relationships in Data Circle Graph (Pie Chart) A graph in which data are represented by disjoint sections of a circular region, with each section representing a part of the whole To make a circle graph 1. Find the fractional part of the total each data category represents. 2. Multiply each fractional part by 360 . This number represents the measure of the central angle for each section.

To make a circle graph: (cont.) 3. Draw a circle and mark the center. 4. Draw a radius to use as the initial side of the first central angle. 5. Divide the circle into sections by drawing central angles with the measures found in step 2.