Scatter Plots

Scatter Plots Scatter plots are similar to line graphs in that they use horizontal and vertical axes to plot data points. However, they have a very specific purpose. Scatter plots show how much one variable is affected by another. The relationship between two variables is called their correlation. Scatter plots usually consist of a large body of data. The closer the data points come when plotted to making a straight line, the higher the correlation between the two variables, or the stronger the relationship. If the data points make a straight line going from the origin out to high x- and y-values, then the variables are said to have a positive correlation. If the line goes from a high-value on the y-axis down to a high-value on the x-axis, the variables have a negative correlation. A perfect positive correlation is given the value of 1. A perfect negative correlation is given the value of -1. If there is absolutely no correlation present the value given is 0. The closer the number is to 1 or -1, the stronger the correlation, or the stronger the relationship between the variables. The closer the number is to 0, the weaker the correlation. So something that seems to kind of correlate in a positive direction might have a value of 0.67, whereas something with an extremely weak negative correlation might have the value -.21. An example of a situation where you might find a perfect positive correlation, as we have in the graph on the left above, would be when you compare the total amount of money spent on tickets at the movie theater with the number of people who go. This means that every time that "x" number of people go, "y" amount of money is spent on tickets without variation. An example of a situation where you might find a perfect negative correlation, as in the graph on the right above, would be if you were comparing the speed at which a car is going to the amount of time it takes to reach a destination. As the speed increases, the amount of time decreases. On the other hand, a situation where you might find a strong but not perfect positive correlation would be if you examined the number of hours students spent studying for an exam versus the grade received. This won't be a perfect correlation because two people could spend the same amount of time studying and get different grades. But in general the rule will hold true that as the amount of time studying increases so does the grade received. Let's take a look at some examples. The graphs that were shown above each had a perfect correlation, so their values were 1 and -1. The graphs below obviously do not have perfect correlations. Which graph would have a correlation of 0? What about 0.7? -0.7? 0.3? -0.3? Click on Answers when you think that you have them all matched up.

  EXAMPLE A history teacher asked her students how many hours of sleep they had the night before a test. The data below shows the number of hours the student slept and their score on the exam. The graph is a scatter plot from the given data. Student Number 1 2 3 4 5

6 7 8 9 10

Hours Slept

8 7 7 8 6 5 7 4 9 7

Test Score

83 86 74 88 76 63 90 60 89 81

a) Approximate a best fit line for the data in the graph above. First sketch a line that closely fits the data. Second, locate two points on the line. They don't have to be one of the original data points. We, will choose, (4,60) and (7,80) for this example. Now find the equation of a line using the previous learned techniques. m = (80-60) / (7-4) m = 20 / 3 m = 20/3 y = mx + b y = 20/3x + b 60 = (20/3)4 + b 60 = 80/3 + b 100/3 = b Thus a best fit equation is: y = 20/3x + 100/3

Pictogram A pictogram (also spelled pictogram) or pictograph is a symbol representing a concept, object, activity, place or event by illustration. Pictography is a form of writing in which ideas are transmitted through drawing. It is a basis of cuneiform and, to some extent, hieroglyphic writing, which uses drawings also as

phonetic letters or determinative rhymes. Pictographs use a symbol or key to represent numbers. Early written symbols were based on pictograms (pictures which resemble what they signify) and ideograms (symbols which represent ideas). They were used by the ancient Chinese culture since around 5000 BC and began to develop into logographic writing systems around 2000 BC. Pictograms are still in use as the main medium of written communication in some non-literate cultures in Africa, The Americas, and Oceania. Pictograms are often used as simple symbols by most contemporary cultures. Pictograms can often transcend languages in that they can communicate to speakers of a number of tongues and language families equally effectively, even if the languages are cultures are completely different. This is why that road signs and similar pictographic material is often applied as a global standard expected to be understood by nearly all. Modern use Pictograms remain in common use today, serving as signs or instructions. Because of their graphical nature and fairly realistic style, they are widely used to indicate public toilets, or places such as airports and train stations. A standard set of pictograms was defined in the international standard ISO 7001: Public Information Symbols. Another common set of pictograms are the laundry symbols used on clothing tags and chemical hazard labels. Pictographic writing as a modernist poetic technique is credited to Ezra Pound, though French surrealists accurately credit the Pacific Northwest American Indians of Alaska who introduced writing, via totem poles, to North America.[1] Pictographs from the Great Gallery, Canyonlands National Park Sample National Park Service pictographs Pictograph from 1510 telling a story of coming of missionaries to Hispaniola Water, rabbit, deer pictograms on a replica of an Aztec Stone of the Sun British Rail passenger safety pictograms at the end of the platform at Meols railway station A pictogram warning against swimming because of crocodiles at the Australia Zoo. "No Dogs!" sign in Spain. The dog illustration is a pictogram. The red circle and bar is an ideogram representing the idea of "no" or "not allowed." thumb|The top traffic sign warns people of horses and riders.