Algebra 1/3/17 Good Wednesday Afternoon! Head on over to GOFORMATIVE! Play while you wait: https://www.mangahigh.com/en-us/math_games/data/representing_data/box_and_whisker_plots

Play while you wait: https://www.mangahigh.com/en-us/math_games/data/representing_data/box_and_whisker_plots

Phone Box Plots on Plotly Line Plots & Histograms Skewed Distributions Agenda Phone Box Plots on Plotly Line Plots & Histograms Skewed Distributions Normal Distributions

Write 4 statements you could conclude from this graph. How do the estimates compare to the actual phone use? Did 50% of people in this class use their phone over 30 hours?

The following data is the number of homeruns scored over 18 seasons. Make a Box Plot on your calculator for the data. Is there an outlier?

Is there an outlier? Q1-(1.5*IQR)= Q3+(1.5*IQR)= IQR is interquartile range, q3-q1=32-22=10 1.5*10=15 So anything above (32+15) or 47 is an outlier Or anything below (22-15) or 7 is an outlier No outliers for this data set.

Histograms A histogram is a bar graph that is used to display the frequency of data divided into equal intervals. The bars must be of equal width and should touch but not overlap. The heights of the bars indicate the frequency of data values within each interval. How many students are in the class? 28 How do you know? Add all the frequencies. How many total throws were attempted? 28*10=280 How many total baskets were made? What was the average number of baskets made? Is most of the data congregated on one side or the other? new word-SKEWED

HINT: Use your TI 84 The correct answer to this question is Option (B). In the histogram, we can see that is the data are skewed to the right. This means there is a good chunk of the data that falls towards the lower end of the graph, but there are also less frequently occurring data points toward the higher end of the graph. In cases where a distribution is skewed to the right, the mean will be higher than the median.

How students performed on this question

Skewed or Normal Distributions Sketch these! Skewed or Normal Distributions http://www.mathsisfun.com/data/skewness.html

Sketch these too!

Yep-sketch this one especially!

Line Plots Or Dot Plots What is being measured? One-variable or two variables? ONE –air quality. What does each dot represent? A city and it’s days of unhealthy air quality. What is meant by SKEWED? What conclusion could you make for air quality of most of these cities? Make a box plot on your calc. Are there any outliers?

The correct answer to this question is Option (C) The correct answer to this question is Option (C). The question asks for a description of the shape of a distribution of numerical data. In order to answer correctly, students must identify both the shape of the distribution (approximately symmetric, skewed toward higher values, or skewed toward lower values) and give an appropriate quantitative measure of center. A distribution is approximately symmetric if you can draw a line in the center of the data set and the parts of the graph on each side of the line are roughly mirror images of each other. Option (A) is incorrect, because if you draw a line at 6 days, the two sides of the graph look very different. The terms skewed toward higher values, skewed right, and positively skewed all mean that the data points at the lower end of the scale are more tightly clustered together while the data points at the higher end of the scale are more spread out. In contrast, if we say a distribution is skewed toward lower values, skewed left, or negatively skewed, we mean that the data points at the higher end of the scale are more tightly clustered together while the data points at the lower end of the scale are more spread out. In this data set, 10 of the cities are clustered at the low end of the scale with 0 to 3 days of unhealthy air quality, while the other 9 cities are spread out between 5 and 12 days, so this distribution is skewed toward higher values and Option (D) is incorrect. This question does not explicitly ask students to calculate the median, but they are required to choose an appropriate quantitative measure of center. Options (A) and (B) are incorrect, because they state that 6 days is the center of this distribution. This value is called the midrange, the point halfway between the minimum of 0 and the maximum of 12. Because the distribution is not symmetric, the midrange is not an appropriate measure of center; there are twice as many cities with fewer than 6 days of unhealthy air quality as there are with more than 6 days. The median of 3 days, the middle value in the data set, better reflects the number of days of unhealthy air quality for a typical city.

Why do you think so many students missed this question Why do you think so many students missed this question? How can we define the word SKEW so that we don’t make the same mistake?

Mean of Histograms I can easily see the frequency for each column, but how do we estimate the mean? In the first bar the range of values is from 2.1-2.5, and the frequency is 4. I could have all four people with a 2.1, 2.2, 2.3, etc. Or there could be a mix. Sol-find midpoint of the interval (2.3) and multiply by frequencies then average.

Mean of Histograms I can easily see the frequency for each column, but how do we estimate the mean? In the first bar the range of values is from 2.1-2.5, and the frequency is 4. I could have all four people with a 2.1, 2.2, 2.3, etc. Or there could be a mix. Sol-find midpoint of the interval (2.3) and multiply by frequencies then average.

Make a histogram from our phone data from yesterday. 21 27.2 48 40.23 16 34 34 31 14 9 70 46.5 37 15 15 20.05 14 23.3 80 41.6 50 42.29 50 35.2 8 17.67 50? 35.2 48 28.6 15 7 78 58.62 80 35.1 52 69.58 11 11 40 54.47 40 57.47 50 41 16 31.44 25 16.989 28 30.07 Class Data Make a histogram from our phone data from yesterday. Is it a normal distribution?

Class Phone Usage Histogram

Online Interactive Textbook Trainer Practice Online Interactive Textbook Trainer Unit 4, Lesson 9.2-9.3 Odds- Check as you go