Graphing Review - make sure to look at your book as you review these notes. Look at the examples
Box and Whisker Plots
Suppose you have a large set of data and you want a display that gives a general idea of how the data clusters together. A box-and-whisker plot displays the median, the quartiles, and outliers of a set of data but does not display any other specific values.
To make a box-and-whisker plot:
Write the data in order from least to greatest
Draw a number lime that can show the data in equal intervals – make sure to have intervals that include the least and the greatest
Find the median – Mark it with a dot below ( or above the number line)
Find the upper quartile ( the median of the numbers above the actual median) Mark it with a dot below ( or above the number line)
Find the lower quartile ( the median of the numbers below the actual median) Mark it with a dot below ( or above the number line)
Mark with a dot the upper extreme – the greatest number
Mark with a dot the lower extreme – the lowest number
Draw a box between the lower quartile and upper quartile. Split the box by drawing a vertical line through the median.
Draw two ‘whiskers’ from the quartiles to the extremes.
50% of all the data will be within the box. 25% will be below and 25% will be above.
A frequency table is a way to show how often an item, a number or a range of numbers occurs.
| number | 1 | 2 | 3 | 4 |
| frequency | 4 | 0 | 5 | 8 |
The range is the difference between the highest number and the lowest. In this case 4-1 = 3
Line Plots help show the spread of the data. When you look at a line plot you can easily see the range, the mode, and any outliers in the data,
Draw a horizontal line segment on grid paper
Make a scale of numbers below the line. The numbers should include the greatest value and the least value of the set of data.
For each piece of data, draw an X above the corresponding number.
Stem and Leaf Plots allow you to easily see the greatest, least, and median values in a set of data.
For example—from class
As of 1997 the following are the ages, in chronological order, at which US Presidents were inaugurated
57,61, 57, 57, 58, 57, 61, 54, 68, 51, 49, 64, 50, 48, 65, 52, 56, 46, 54, 49, 50, 47, 55, 55, 54, 42, 51, 56, 55, 51, 54, 51, 60, 62, 43, 55, 56, 61, 52, 69, 64, 46
To make a stem-and-leaf plot:
Write the data in order from least to greatest
Find the least and greatest values
Choose stem values that will include the extreme values. For this graph, it makes sense to use tens.
Write the tens vertically from least to greatest. Draw a vertical line to the right of the stem values.
Separate each number into stems (tens – in this case) and leaves (ones- in this case). Write each leaf to the right of its stem in order from least to greatest.
Write a key that explains how to read the steams and leaves.
Scatter Plots
Suppose you want to analyze two sets of data to see how closely they are related. On a scatter plot you plot corresponding numbers from two sets of data as order pairs (x,y). You then decide if they are related by determining how close they come to forming a straight line.
For example, here is a frequency table of the number of hours studied and grades of a student
| study hours | 1.5 | 1 | 3 | 2.5 | 1.5 | 4 | 3.5 |
| grade on test | 75 | 71 | 88 | 86 | 80 | 97 | 92 |
To make the scatter plot
Decide which set of numbers you will plot on each axis and label the axis. In this case, The study time ( in hours) would be the X-axis and the Grade would be the Y-axis.
Choose a scale for each axis.
Plot corresponding numbers as ordered pairs. For example (1.5, 75) and (1, 71) are the first two from the table above.
The dots on the scatter plot are close to forming a straight line ( going up) so this is a strong positive correlation.
If the line formed was going down—it would be a negative correlation
and if you could not determine any line- it would be no correlation.
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