MEAN DEVIATION
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The mean deviation is a measure of how spread out values are from the average. It is calculated by: 1) Finding the mean of all values. 2) Calculating the distance between each value and the mean. 3) Taking the average of those distances. This provides the mean deviation, which tells us how far on average values are from the central mean. Examples show calculating mean deviation for both grouped and ungrouped data sets.
MEAN DEVIATION
- 2. What is mean deviation? The mean deviation is the first measure of dispersion that we will use that actually uses each data value in its computation. It is the mean of the distances between each value and the mean. It gives us an idea of how spread out from the center the set of values is.
- 3. How can we use mean deviation in real life? Investments 120 100 80 WONDERLAND 60 NEVERLAND 40 FANTASIA 20 0 JANUARY FEBRUARY MARCH APRIL
- 4. 88. WONDERLAND = 85+85+89+95/4 = 5 MEAN DEVIATION = 3.5 NEVERLAND = 75+75+80+85=/4 = MEAN DEVIATION = 3.75 FANTASIA = 87+90+96+97/4= MEAN DEVIATION = 4 78.75 92. 5
- 5. Formula for Mean Deviation: (ungrouped data) MD Where, μ = mean x n x = each value N = number of values
- 6. Mean Deviation -The mean of the distances of each value from their mean. Three steps on finding the mean: 1) Find the mean of all values. 2) Find the distance of each value from that mean. 3) Find the mean of those distances.
- 8. Step 2: Find the distance of each vaue from the mean. Value Distance from 9 3 6 6 3 6 3 7 2 8 1 11 2 15 6 16 7 6+3+3+2+1 = 2+6+7 15 = 15 It tells us how far, on average, all values are from the middle.
- 9. 3.7 5
- 10. Exercises : 1) A booklet has 12 pages with the following numbers of words: 271, 354, 296, 301, 333, 326, 285, 298, 327, 316, 287 and 314 What is the mean deviation of the number of words per page?
- 11. Step 1: Find the mean. Raw Data: 271, 354, 296, 301, 333, 326, 285, 298, 327, 316, 287, 314 271 354 296 301 333 326 285 298 327 12 30 9 2/22/2014 316 287 314
- 12. Step 2: Find the Absolute Deviations. x x 271 354 296 301 333 326 285 298 327 316 287 314 38 45 13 8 24 17 24 11 18 7 22 5 x 232
- 13. Step 3: Find the Mean Deviation M .D . x 232 N 12 19.33
- 14. Formula for Mean Deviation: (grouped data) f x MD Where, μ = mean f x = each value f = frequency
- 15. Three steps on finding the mean: 1) Find the mean by using the formula fx f 2) Solve for x and multiply it to the frequency of each class. Find the f x 3) Divide the answer of the f to
- 16. Step 1: Find the mean by using the given formula: fx x f 0 1 2 3 4 5 6 4 12 8 2 1 2 1 f fx 0 12 16 6 4 10 6 f 30 fx So, fx f 54 54 30 1.8
- 17. Step 2: Complete the table. x f fx 0 1 2 3 4 5 6 4 12 8 2 1 2 1 0 12 16 6 4 10 6 f 30 fx x f x 1.8 0.8 0.2 1.2 2.2 3.2 4.2 54 7.2 9.6 1.6 2.4 3.3 6.4 4.2 f x 33 . 6
- 18. Step 3: Divide the answer of to the f summation of f x 33 . 6 f 1 . 12 30 Mean Deviation = 1.12
- 19. Exercises : The children in a class did a survey of the number of siblings (brothers and sisters) each of them had. The results are recorded in the following table. Calculate the mean deviation.
- 20. Step 1: Find the mean by using the given formula: fx x f 0 1 2 3 4 5 6 7 8 9 3 6 8 5 4 2 1 0 0 1 f fx 0 6 16 15 16 10 6 0 0 9 f 30 fx So, fx 78 f 30 2.6 78
- 21. Step 2: Complete the table. x f fx 0 1 2 3 4 5 6 7 8 9 3 6 8 5 4 2 1 0 0 1 0 6 16 15 16 10 6 0 0 9 f 30 fx x f x 2.6 1.6 0.6 0.4 1.4 2.4 34 4.4 5.4 6.4 78 7.8 9.6 4.8 2.0 5.6 4.8 3.4 0 0 6.4 f x 44 . 4
- 22. Step 3: Divide the answer of to the f summation of f x 44 . 4 f 1 . 48 30 Mean Deviation = 1.4 8