Which is the average of the sum of absolute difference of each measure from the mean?
The measure of spread represents the amount of dispersion in a data-set. i.e how spread-out are the values of data-set around the central value(example- mean/mode/median).It tells how far away the data points tend to fall from the central value. Show
Distribution of Data Using the above diagram, we can infer that the narrow distribution represents a lower spread, and the broad distribution represents a higher spread. RangeThe range is the simplest measure of variation. It is defined and calculated as the difference between the largest and smallest values of the data-set. Range = largest value – smallest value
ExamplesExample 1: The data given are: 8, 10, 4, 1, 15. Calculate the range of the given data? Solution:
Example 2: What is the range of these integers? 14, -18, 7, 0, -5, -8, 15, -10, 20 Solution:
Example 3: Calculate the range of the given data: 8, 10, 5 , 14 , 42, 3566 Solution:
Mid-RangeThe mid-range is the value midway between the largest and smallest value of a data-set. It is calculated as the mean of the largest value and smallest value of the data-set. Mid-Range = (largest value + smallest value)/2 ExamplesExample 1: The data given is 8, 10, 5, 9, 11. Calculate the mid-range of the given data? Solution:
Example 2: You take 7 statistics tests over the course of a semester. You score 94, 88, 74, 84, 91, 87 and 79. What is the mid-range of your scores? Solution:
Example 3: The height of 8 students in centimeters is given as 120, 132, 117, 126, 110, 135, 150, and 143. Calculate the mid-range of the given data? Solution:
Mean Absolute Deviation (MAD)The mean absolute deviation (MAD) of a data-set is the average distance between each data point of the data-set and the mean of data. i.e it represents the amount of variation that occurs around the mean value in the data-set. It is also a measure of variation. It is calculated as the average of the sum of the absolute difference between each value of the data-set and the mean. MAD = (∑ |xi – mean| ) ÷ n where 1 < i < n and n is the number of data-points in the data-set. ExamplesExample 1: The data-set is 11 , 15 , 18 , 17 , 12 , 17. Calculate the mean absolute deviation of the given data-set? Solution:
Example 2: The following table shows the number of oranges that grew on Nancy’s orange tree each season
Find the mean absolute deviation (MAD) of the data set? Solution:
Example 3: Consider the following data-set
Calculate the mean absolute deviation of the given data? Solution:
How do you find the sum of absolute deviations from the mean?Step 1: Calculate the mean. Step 2: Calculate how far away each data point is from the mean using positive distances. These are called absolute deviations. Step 3: Add those deviations together.
How do you find the absolute difference between means?The absolute difference between two variables, for example two means or proportions is simply one subtracted from the other. It is often written as δB,A or δabs = μ1 - μ2, equivalently δabs = p1 - p2 for proportions.
What is the difference between mean and mean absolute deviation?The Mean Absolute Deviation (MAD) of a set of data is the average distance between each data value and the mean. The mean absolute deviation is the "average" of the "positive distances" of each point from the mean. The larger the MAD, the greater variability there is in the data (the data is more spread out).
What is also called as average deviation?The average deviation of a set of scores is calculated by computing the mean and then the specific distance between each score and that mean without regard to whether the score is above or below the mean. It is also called an average absolute deviation.
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