How to Find the Standard Deviation, Variance, Mean, Mode, and Range for any Data Set
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In this section, the speaker introduces the process of finding standard deviation, variance, mean, median, mode, and range for given data by first arranging the data in ascending order.
Finding Median
- The median is identified as the middle number in a dataset. In this example, the median is 15 since there are three values on each side.
Determining Mode and Range
- Mode refers to the value that appears most frequently. Here, 11 and 20 are modes as they both occur twice.
- Range is calculated by subtracting the smallest value (7) from the largest value (28), resulting in a range of 21.
Calculating Mean
- Mean (x̄) is computed by summing all data values and dividing by the total number of values. For this dataset, x̄ equals 16.
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This part focuses on further calculations involving mean deviations and squaring those deviations for variance determination.
Computing Deviations
- Deviations (X - x̄) are found by subtracting each data point from the mean. For instance, 7 - 16 = -9.
Squaring Deviations
- Squaring these deviations (-9², -5², etc.) yields new values: 81, 25, etc., which are then summed up to get Σ(X - x̄)² as 308.
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This segment delves into calculating variance and standard deviation based on previously obtained results.
Determining Variance
- Variance (S²) is computed using Σ(X - x̄)² divided by n - 1. For this dataset with n = 7, variance equals approximately 51.333.
Finding Standard Deviation
- Standard deviation (S), represented as √Σ(X - x̄)² / n -1 , results in S ≈ 7.65 after calculations with Σ(X - x̄).
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The final part involves finding the median through averaging when two middle numbers exist in a dataset.
Calculating Median