Bell Ringers Calculate the mean median and mode for the following sets of data. 1.15, 16, 19, 6, 16, 17, 19 Mean: Median: Mode: 2. 68, 74, 20, 45, 96, 84 Mean: Median: Mode: 3. 22, 33, 56, 78, 22, 95, 33, 56 Mean: Median: Mode: , 89, 147, 86, 114, 103, 88 Mean: Median: Mode:

Measures of Variability

Today I will be able to define variability. Today I will be able to define and calculate range, absolute deviation, and interquartile range. Today I will be able to use measures of variability to discuss data.

What is Variability Variability is a measure of the spread of a data set. Variability refers to how spread out a group of data is. In other words, variability measures how much your scores differ from each other. Variability is also referred to as dispersion or spread. Data sets with similar values are said to have little variability, while data sets that have values that are spread out have high variability.

What data is collected to find variability? When examining variability in data we calculate the various measures of variability: range, mean absolute deviation, and interquartile range.

What is range? The range is the simplest measure of variability. How do we find range? You take the smallest number and subtract it from the largest number to calculate the range. What does range tell us? This lets us know the spread of our data. Although it is simple to calculate, the range is sensitive to outliers, or values that are significantly higher or lower than the rest of the data set, and should not be used when outliers are present

How do we solve for range? Amber took 7 math tests in the first nine weeks. What is the range of her test scores? 89, 73, 84, 91, 87, 77, 84 Step 1: order the numbers from least to greatest. 73, 77, 84, 84, 87, 89, 91 Step 2: Subtract the highest data point and the lowest data point = 18 The range of the data is 18

Find the range for this data The Mielke family drove through 6 Midwestern states. The gas prices varied from state to state. What is the range of gasoline prices? $1.79, $1.61, $1.96, $2.09, $1.84, $1.75

What is the absolute mean deviation? The mean absolute deviation is the average amount that each number is away from the mean of the data set. The mean absolute deviation because it helps us determine if the mean is useful.

How to find the Mean Absolute Deviation 1) Find the mean of the data. 2) Subtract the mean from each data entry. 3) Take all of the subtractions, make them positive, and find their average.

Find the Absolute Mean Deviation The following are scores on a Math test. Find the mean absolute deviation. 80, 85, 81, 0, 85, 90, 87, 92 Step 1: find the mean of the data: Step 2: find the deviations of the data from the mean: Step 3: take the absolute value of each deviation and find the average:

What does the Absolute Mean Deviation Tell Us The mean absolute deviation for this test is What does this tell us? Is the mean relevant for this data? When the mean absolute deviation is large, that means that the mean is not relevant. This is because there is an outlier.

Find the Absolute Mean Deviation Emma played five games. These are her scores. What is the absolute mean deviation and what does it tell us? 30, 20, 15, 20, 20, 25

What is the interquartile range? The interquartile range (IQR), or the middle fifty, is the range for the middle fifty percent of the data. The IQR only considers middle values, so it is not affected by outliers.

How do we calculate IQR? List the data in numerical order Find the median Place brackets around the numbers above and below the median. Do not place brackets around the median Locate Q3 and Q1 – The median of the lower set of data in the brackets is Q1 – The median of the higher set of data in the brackets is Q3 Plug in the values into the equation IQR = Q3 -Q1 to find the IQR

Find the IQR Blake received the following grades in math class: 83, 100, 71, 90, 81, 52, 85, 99, 75, 90, 89, 100, 55. Find the IQR Step 1: Put the numbers in numerical order 52, 55, 71, 75, 81, 83, 85, 89, 90, 90, 99, 100, 100 Step 2: Find the median 52, 55, 71, 75, 81, 83, 85, 89, 90, 90, 99, 100, 100 Step 3: Place brackets around the numbers above and below the median. Do not place brackets around the median (52, 55, 71, 75, 81, 83) 85 (89, 90, 90, 99, 100, 100) Step 4: Locate Q3 and Q1: The median of the lower set of data in the brackets is Q1. The median of the higher set of data in the brackets is Q3 (52, 55, 71, 75, 81, 83) = (71+75) / 2 = 73 is Q1 (89, 90, 90, 99, 100, 100) = (90+99) / 2 = 94.5 is Q3 Step 5: Plug in the values into the equation IQR = Q3 -Q1 to find the IQR = 21.5

Find the IQR The girls jumped the following distances in the long jump: 95, 63, 49, 75, 87, 102, 125, 47, 49, 98