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Asked by Rakesh Last Modified
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To find the mean deviation about the mean, we first need to calculate the mean of the given data. We can do this by using the formula:
Mean (π₯Μ) = ∑(ππ × π₯π) / ∑ππ
Where ππ represents the frequency and π₯π represents the corresponding size.
Let's calculate the mean:
Mean (π₯Μ) = (3×1 + 3×3 + 4×5 + 14×7 + 7×9 + 4×11 + 3×13 + 4×15) / (3 + 3 + 4 + 14 + 7 + 4 + 3 + 4) = (3 + 9 + 20 + 98 + 63 + 44 + 39 + 60) / 38 = 336 / 38 ≈ 8.8421 (rounded to 4 decimal places)
Now that we have the mean, let's find the mean deviation about the mean using the formula:
Mean Deviation = ∑(ππ × |π₯π - π₯Μ|) / ∑ππ
Where |π₯π - π₯Μ| represents the absolute deviation of each size from the mean.
Let's calculate the mean deviation:
Mean Deviation = (3×|1 - 8.8421| + 3×|3 - 8.8421| + 4×|5 - 8.8421| + 14×|7 - 8.8421| + 7×|9 - 8.8421| + 4×|11 - 8.8421| + 3×|13 - 8.8421| + 4×|15 - 8.8421|) / 38 = (3×7.8421 + 3×5.8421 + 4×3.8421 + 14×1.8421 + 7×0.1579 + 4×2.1579 + 3×4.1579 + 4×6.1579) / 38 = (23.5263 + 17.5263 + 15.3684 + 25.7894 + 1.1053 + 8.6316 + 12.4737 + 24.6316) / 38 ≈ 128.9936 / 38 ≈ 3.3946 (rounded to 4 decimal places)
So, the mean deviation about the mean for the given data is approximately 3.3946.
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