Data Representation Box Plots Histograms or Bar Graphs

Data Representation Box Plots Histograms or Bar Graphs Stem and Leaf Plots Mean Average Deviation

Data • Taken from the MTI Course given by Boise State Animal Speed k/h Bison 50 Jackal 56 Cat 48 Lion 81 Cheetah 113 Mule Deer 56 Chicken 15 Pig 18 Coyote 69 Pronghorn Antelope 98 Elephant 40 Quarter Horse 77 Elk 73 Rabbit 56 Giraffe 52 52 Squirrel 19 Gray Fox 68 Warthog 48 Greyhound 63 Wildebeest 81 Grizzly Bear 48 Wild Turkey 24 Human 45 Zebra 65

Questions taken from Boise State MTI course for the rest of the slides. • How might you represent these data? https: //www. youtube. com/watch? v=_7 m 0 Q_m 2 ppg Create a stem and leaf plot for the animal data Stem 1 1 Leaf 5 8 Arranging all of the data points this way will allow you to see the distribution of the data more easily. The stem is the first number for the rate of the animal and the leaf Is the second number. Now you fill out all of the data.

Box and Whisker Plot • Make a box-and-whisker plot of the speeds of all the animals. • Arrange the data in sequential order and organize into quartiles to review the skew of the data. • The skew of the data refers to how the data looks, whether it is centered or justified left or right.

Box and Whisker Plot https: //www. youtube. com/watch? v=M 0 Fi 0 ijn. Js 15 18 19 24 40 45 48 48 48 50 52 56 56 56 63 65 68 69 73 77 81 81 98 113 There are 24 points of data. Therefore the median because it is even is going to be two points. In this case the median is 56 coded in red. The first and quartile is halfway between 15 and 56 or 45 coded in blue. The fourth quartile begins half way to the right of the second 56 coded in red and 113 at the end or 73 coded in purple.

Box and Whisker Plot https: //www. youtube. com/watch? v=M 0 Fi 0 ijn. Js 15 18 19 24 40 45 48 48 48 50 52 56 56 56 63 65 68 69 73 77 81 81 98 113 Now that we have coded our quartiles we need to give it the appropriate range quality on a number line. Our range is from 15 to 113 15 45 56 64 73 113

Box and Whisker Plot https: //www. youtube. com/watch? v=M 0 Fi 0 ijn. Js 15 18 19 24 40 45 48 48 48 50 52 56 56 56 63 65 68 69 73 77 81 81 98 113 Notice that the box which is where the 2 nd and 3 rd quartile is shows a skew to the left side and that the space reflect the distances between quartiles. The red line indicates the position of the median. Does the outcome surprise you and why? The orange numbers shows you the distance between the points and are not normally included in a box-and-whisker plot 30 15 9 45 8 56 64 9 40 73 113

Histograms • Histograms or Bar graphs are used to organize data into categories. For example black, white and 8 red. 7 6 5 Series 1 4 Column 1 3 Series 3 2 1 0 Black rock Red Rock Green Rock Grey Rock

Measures of Central Tendency

Mean Median and Mode Measures of Central Tendency x • 0 10 x x x x 20 30 40 50 60 70 80

Mean Median and Mode Continued The mode is the data point that occurs the most. The mode of this data is 40. x • 0 10 x x x x 20 30 40 50 60 70 80

Mean Median and Mode Continued The median is the middle of the data. It helps to string out the data. 10, 20, 30, 30, 40, 40, 50, 50, 60, 70. The median is 40. x • 0 10 x x x x 20 30 40 50 60 70 80

Mean Median and Mode Continued The mean is related to the distance between the data points. Imagine that each data point is a sticky note. You could divide the distance between 10 and 70 and arrive at forty. If you this over and over you would eventually arrive at the mean. The algorithm to solve it simply States , add all the data points and divide by the number of data points. x • 0 10 x x x x 20 30 40 50 60 70 80

Mean Median and Mode Continued Mean 10 + 20+30+30+30+40+40+50+50+50+60+60+70 = 640 Dividing by 640 by 16 you get the mean of 40. x • 0 10 x x x x 20 30 40 50 60 70 80

Mean Median and Mode Continued Challenge what will happen to the mean if we changed 70 to 90? Would the mean move To the right or the left? How do you know? x • 0 10 x x x x 20 30 40 50 60 70 80

Mean Median and Mode Continued The total of the data points now is 660 and 660 divided by 16 is 41. 25 so the curve is skewed to the right. x • 0 10 x x x x x 20 30 40 Mean = 41. 25 x x x 50 60 70 x 80 90

Mean Median and Mode Continued The spread of the data deals with the distance between data points and the relation to the mean. Think about which of the two data distributions are more spread out. Is it the one with a balanced curve of the one that is skewed to the right? Take a moment to think about it. x • 0 10 x x x x 20 30 40 50 60 70 80

Mean Absolute Deviation • First we must find the mean. 10 + 30 +70 = 110 divided by 3 = 36. 6 repeating. x x x 10 30 70

Mean Absolute Deviation • Once we have the mean we then find the distance between the mean and the data points. I rounded the mean to 36. 7 -10 = 26. 7 36. 7 -30 = 6. 7 70 - 36. 7 = 33. 3 x x x 10 30 70

Mean Absolute Deviation • Now add the distances up and divide by the number of distances. 26. 7 + 33. 3 = 66. 7 divided by 3 = 22. 23 repeating or 22. 23 There for the MAD is 22. 23 x x x 10 30 70

Mean Absolute Deviation Application • Making comparisons between data sets and making meaning out of a single data set is inferential statistics or drawing inferences from the data. If the following two schools both had the following data sets and are teaching the same curriculum. Which one is getting more consistent results even if the averages are the same. MAD would be a very useful statistic in this case. X x x x *** Be careful not to make judgments based on one statistic i. e. mean, median, mode, or MAD. Look at the data as many ways as you can to include models like above. Your looking for the story that the data is trying to tell you.

Mean Absolute Deviation • What this allows us to do is compare the spread of a set of data to another. If a set of data has a mad of 22. 23 versus a second data distrubution with a MAD of 5. 6 which one is clumped more closely together? X x x x The larger the mad the more spread out the data.

Activity • We will take samples of the rock in the parking lot and create stem and leaf, box plot, histograms and calculate MAD to examine our data.

Activity Probability • Map out the combinations of outcomes that two dice can result in. What does the shape look like? Does it remind you of anything? • Now roll the pair of dice 50 times and keep track of your outcomes. What shape does it make. • Is there a difference between experimental and theoretical probability? • If we kept rolling the dice up to a 1000 time would it be more or less like the experimental probability?

Activity • What is theoretical probability with a coin that I will get heads or tails? • Now flip the coin 50 times and record the results. Does the experimental probability match the experimental probability?

Outcomes from 0 to 1 • Think of 1 as 100% • . 5 would be a 50% • . 05 would be a 5% chance