1. Standard Deviation

2. 43210 In addition to level 3.0 and above and beyond what was taught in class, the student may: · Make connection with other concepts in math · Make connection with other content areas. The student will summarize, represent, and interpret data on a single count or measurement variable. - Comparing data includes analyzing center of data (mean/median), interquartile range, shape distribution of a graph, standard deviation and the effect of outliers on the data set. - Read, interpret and write summaries of two-way frequency tables which includes calculating joint, marginal and relative frequencies. The student will be able to: - Make dot plots, histograms, box plots and two-way frequency tables. - Calculate standard deviation. - Identify normal distribution of data (bell curve) and convey what it means. With help from the teacher, the student has partial success with summarizing and interpreting data displayed in a dot plot, histogram, box plot or frequency table. Even with help, the student has no success understandin g statistical data. Focus 6 Learning Goal – (HS.S-ID.A.1, HS.S-ID.A.2, HS.S-ID.A.3, HS.S-ID.B.5) = Students will summarize, represent and interpret data on a single count or measurement variable.

3. Normal Distribution  There are many cases where data tends to be around a central value with no bias left or right. This is called a Normal Distribution.  The “Bell Curve” is a Normal Distribution.  It is often called a “bell curve” because it looks like a bell.  The Normal Distribution has mean = median = mode.

4. Standard Deviation  The standard deviation is a measure of how spread out numbers are.  Generally, this is what we find out: 68% of values are within 1 standard deviation of the mean. 95% of values are within 2 standard deviations of the mean. 99.7% of values are within 3 standard deviations of the mean.

5. Learn more about Normal Distribution and Standard Deviations  The video to play as at the bottom of the screen.

6. Refresher on 1, 2 and 3 standard deviations from the mean.

7. IQ Scores  An IQ score is the score you get on an intelligence test. The scores follow a normal distribution.  What percent of people have an IQ score between 85 and 115?  What percent of people have an IQ score between 70 and 85?  What percent of people have an IQ score above 130?  In a population of 300 people, how many people would you expect to have an IQ score above 130? 68% 13.5% 2.5% 0.025(300) = 7.5, 7 or 8 people in a group of 300 would have an IQ score greater than 130.

8. Standard Deviation  Example: 95% of students at school are between 1.1 m and 1.7 m tall. Assuming the data is normally distributed, calculate the mean and standard deviation.  The mean is halfway between 1.1m and 1.7m.  Mean = (1.1 + 1.7)/2 = 1.4 m  95% is two standard deviations either side of the mean (a total of 4 standard deviations) so:  1 standard deviation = (1.7 – 1.1)/4  = 0.6/4  = 0.15 m Mean Multiply 0.15 by 2 then 3 to get the 2 nd and 3 rd intervals. Each interval is 0.15 below or above the mean.