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:
What does mean absolute deviation measure explain how do you find the MAD for a set of data?Mean absolute deviation (MAD) of a data set is the average distance between each data value and the mean. Mean absolute deviation is a way to describe variation in a data set. Mean absolute deviation helps us get a sense of how "spread out" the values in a data set are.
How do you find the MAD in a set of data?Take each number in the data set, subtract the mean, and take the absolute value. Then take the sum of the absolute values. Now compute the mean absolute deviation by dividing the sum above by the total number of values in the data set. Finally, round to the nearest tenth.
How do you calculate MAD deviation?Median Absolute Deviation-subtract the median from each value in the data set and make the difference positive. Add up these quantities and divide by the number of values in the data set. Mean Absolute Deviation-subtract the mean from each value in the data set and make the difference positive.
How does the mean absolute deviation MAD of the data in set 1?How does the mean absolute deviation (MAD) of the data in set 1 compare to the mean absolute deviation of the data in set 2? The MAD of set 1 is 5 less than the MAD of set 2. Without calculating any statistics, Jadyn knows that data set 1 would have the least mean absolute deviation among the three sets.
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