### MS 150 Statistics q13 fall 2006 • Name:

Hue angle data
Hue nameHue angle°
red9
orange-red17
red-orange24
red-orange24
dark orange26
orange30
yellow-orange36
orange-yellow43
goldenrod48
gold52
yellow64
green-yellow77
chartreuse88
green111
mint137
aquamarine165
cyan184
deep sky blue200
royal blue217
blue230
blue236
blue239
indigo250
purple270
magenta303

#### Part I: Basic Statistics

Color can be described in many different ways. There are color words such as red, orange, yellow, green, and blue. In optical physics each color is described by a wavelength and frequency of light.

A third way to describe color is by using a color wheel or circle. The word hue is used for the word color when working with a color wheel. On a color wheel the colors are arranged in a circle in the same order that the colors appear in a rainbow. While in art class one learns that the primary colors for paint are red, yellow, and blue; the primary colors for light are different. The primary colors of light are red, green, and blue.

Red, the first color in the rainbow, is placed at the top and is assigned a color angle (or hue angle) of 0°. Once around a circle is 360°. Green is placed one third of the way around the circle at 120°. Blue is placed two-thirds of the way around the circle at 240°.

In the first section the image of a rainbow was analyzed from red to purple, with the hue angles being recorded at equal distances across the face of the rainbow.

Data sheet

For the hue angle data given in the table:

1. _________ What level of measurement is the hue angle data?
2. _________ Determine the sample size n.
3. _________ Calculate the sample mean x.
4. _________ Determine the median.
5. _________ Determine the mode.
6. _________ Determine the minimum.
7. _________ Determine the maximum.
8. _________ Calculate the range.
9. _________ Calculate the sample standard deviation sx.
10. _________ Calculate the sample Coefficient of Variation.
11. _________ Determine the class width. Use 6 bins (classes or intervals)
12. Fill in the following table with the class upper limits in the first column, the frequencies in the second column, and the relative frequencies in the third column
BinsFrequencyRelative Frequency f/n
___________________________
___________________________
___________________________
___________________________
___________________________
___________________________
Sums:__________________
13. Sketch a histogram of the relative frequency data on the back of the paper.
14. __________________ What is the shape of the distribution?