A.9: The student given the data, will interpret variation in real-world contexts and calculate and interpret mean, absolute deviation, standard deviation, and z-scores

 Average of the absolute values of the differences between the mean and each value in the data set

Step 1: Find the mean, Step 2: Find the sum of the absolute values of the differences between each value in the set of data and the mean Step 3: Divide the sum by the number of values in the set of data

 Each person that visited the Comic Book Shoppe’s website was asked to enter the number of times each month they buy a comic book. The received the following responses: 2, 2, 3, 4, 14.  Find the mean absolute deviation

 Mean = 5

 |2 – 5| + |2 – 5| + |3 – 5| + |4 – 5| + |14 – 5| = =18

 18 ÷ 5 = 3.6

n = number of elements μ = mean (mu)

 The prom committee kept count of how many tickets it sold each day during lunch: 12, 32, 36, 41, 22, 47, 51, 33, 37, 49 Find the mean absolute deviation

When there are a large number of values in a data set, the frequency distribution tends to cluster around the mean

In the last video we talked about one measure of dispersion (or, a tool by which we are able to measure the “spread” or behavior of data in relation to it’s mean). Today we will talk about two others: the Standard Deviation and the Variance.

 Shows how the data deviates from the mean  σ- lower case Greek symbol, sigma

 The square of the standard deviation  σ²

 Step 1: Find the Mean  Step 2: Find the square of the difference between each value in the set of data and the mean. Sum the squares and divide by number of values in the data set, thereby giving you the Variance  Step 3: Take the square root of the Variance to get the Standard Deviation

n = number of elements μ = mean σ = standard deviation

 3, 6, 11, 12, and 13 Step 2: σ² =(3-9)²+(6-9)²+(11–9)²+(12–9)²+(13-9)² = (-6)² + (-3)² + 2² + 3² + 4² = = 74 VarianceStandard Deviation

 6, 10, 15, 11, 12 and 8 VarianceStandard Deviation

 92, 84, 71, 83, and 100

 An Algebra I class has the following scores: Find the Standard Deviation and Variance for the scores in this class!

In this video we will talk about another measure of dispersion. The Z-score is a method by which we are able to compare data entries in two separate sets by comparing them to their respective sets. Sounds complicated, but it isn’t!

Zach is trying to figure out how he did on his tests in comparison to his friends. The tests he took were Math and History. The following tables show the scores from both of his classes, with his scores highlighted in red.

Math Test Grades History Test Grades Mean = 92 How does he compare with his peers and how do we quantify that accurately?

Math Test ScoresHistory Test Scores How many Standard Deviations is he from the mean in each data set? Since 92 – 6.3 = 85.7, he is approximately 1 standard deviation BELOW the mean Since = 70.6, he is approximately 1 standard deviation ABOVE the mean

Math Test ScoresHistory Test Scores S.D. -1 S.D.

 Represents the number of standard deviations that a given data value is from the mean

For instance… A Z-Score of 3 means you’re three S.D. above the mean A Z-Score of -3 means you’re three S.D.s below the mean

 The mean height of a 15-year-old boys in the city where Isaac lives is 67 inches, with a standard deviation of 2.8 inches. Find interpret the z-score of a height of 73 inches. Therefore, 73 is about 2.14 standard deviations more than the mean of the distribution.

 The weight of chocolate bars from a particular chocolate factory have a standard deviation of.1 ounce. The z-score corresponding to a weight of 8.17 ounces is 1.7. What is the mean for the weight of these chocolate bars? The mean is 8 ounces!

1. Books in the library are found to have average length of 350 pages with standard deviation of 100 pages. What is the z-score corresponding to a book of length 80 pages? 2. A group of friends compares what they received while trick or treating. They find that the average number of pieces of candy received is 43. The z-score corresponding to 20 pieces of candy is What is the standard deviation?

Is there a relationship between the total amount of fat in a snack and how many calories there are?

Calories Fat (grams)

Correlation Coefficient (r): This value measures the strength of a certain line of best fit for a given set of data. This is number is generated by your calculator! Negative Correlation (r=-1): This means that it is a perfect negative fit, that is, as x increases, y decreases. Positive Correlation (r=1): This means that it is a perfect positive fit, that is, as x increases, y increases. No Correlation (r=0): This means that there is no correlation between the two values.

Calories Fat (grams) Strong Correlation

If a snack had 12 grams of fat in it, how many calories would that be? If a snack had 1200 calories, how many grams of fat might it have?

1.Create a scatter plot in your notebook (free hand or graph paper) using the following data. 2.What is the line of best fit for this set of data? (To the nearest hundredth) 3.What is the correlation coefficient? (to the nearest hundredth) 4.If the amount of money in sales is $350, what is the approximate temperature?

How many elements are below the mean? How many elements are above the mean? How many elements fall within one standard deviation of the mean?