Marcos was introduced to the Normal Distribution today. It is represented as a bell curve. The Emperical Rule says that 68% of the data lies within +/- 1 standard deviation from the mean. 95% lies within 2 standard deviations, and 99.7% lies within 3 standard deviations. Marcos worked on exercises to find how much data lies within certain z-scores. He did an excellent job of listening to the video explanation, and independently answering the questions.
Marcos continued watching Algebra Nation teaching videos about Statistical Studies. He took notes and learned to identify population, sample, variable of interest, parameter, and statistic of interest. There are different ways to gather data: sample surveys, observational surveys, and experiments. An experiment applies treatment to a situation. The three principles of experimental design are Randomization, Replication, and Control. Marcos answered questions where he had to identify the type of situation, and identify any problems with the collection of data. He also had to determine whether or not a sampling method was biased or not.
I started a section on Statistics and Parameters today. We are using Algebra Nation videos from an Algebra 2 course to help Marcos learn the material. The information introduced dealt with looking at samples to help us understand what is happening in a population. Marcos had notes to fill out, and he did a great job listening and understanding the concepts that were defined.
Marcos worked on exercises that represented quadratic equations as graphs. He had to answer questions about what the graphs meant, and find a variety of values by either looking at the graphs, or plugging numbers into the equations. He did an excellent job of answering the questions.
Using a dot graph and a frequency chart, Marcos listed data and found the following: Mean, Median, Mode, Upper Quartile, Lower Quartile, Interquartile Range, and Standard Deviation. Finding the Standard Deviation involved taking each data point, subtracting it from the mean, squaring that difference, then adding all of those squared values up and dividing by one less than the number of data points. This results in the variance. The square root of the variance is the standard deviation.
We defined mode, median, mean, lower quartile, upper quartile, and interquartile range. Marcos now has a list of the definitions on his board. Given a list of data, he worked through 3 exercises where he had to find all of the above for the data. Mode: data that occurs most, Median: data in the middle, mean: average, lower quartile: the median of the lower half of data, upper quartile: the median of the upper half of data, interquartile range: the difference between the upper and lower quartile. Marcos was focused!
To calculate standard deviation, we must do the following:
1. Find the mean of our set of data...
2. Take the difference of each piece of data and the mean...
3. Square each of them...
4. Sum the squares in the previous step...
5. Divide by the number of pieces of data...
6. This gives us the variance. To find the Standard Deviation, take the square root.
Marcos watched a few examples of this, and then worked through a few exercises on his own. He did a good job with it!
We looked at Khan Academy videos about Interquartile Range, Median, and Measures of Spread. Measures of Spread are the Range, Variance, and Standard Deviation. They show us how data is spread out. The median is the number listed in the middle when they are put in ascending order. We can then find the median of each half of data. The difference between these 2 is the interquartile range.
