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Using the formula, find the coefficient of skewness for each distribution, and describe the shape of the distribution.

a. Mean = 10, Median = 8, Standard Deviation = 3

b. Mean = 42, Median = 45, Standard Deviation = 4

c. Mean = 18.6, Median = 18.6, Standard Deviation = 1.5

d. Mean = 98, Median = 97.6, Standard Deviation = 4

Answer :

Final answer:

The coefficient of skewness is calculated by (Mean - Median) / Standard Deviation. This value depicts the extent and direction of skew (departure from horizontal symmetry) in the data. Our results vary from right skewed, to left skewed, to almost symmetrical distributions.

Explanation:

The coefficient of skewness can be found by using the formula (Mean - Median) / Standard Deviation. By applying this formula, we find:

  1. For distribution a, the skewness coefficient is (10 - 8) / 3 = 0.67. A positive value indicates right-skewed or positively skewed distribution.
  2. For distribution b, the skewness coefficient is (42 - 45) / 4 = -0.75. A negative value informs us that the distribution is left-skewed or negatively skewed.
  3. For distribution c, the skewness coefficient is (18.6 - 18.6) / 1.5 = 0. This indicates a symmetrical distribution.
  4. For distribution d, the skewness coefficient is (98 - 97.6) / 4 = 0.1. As the value is close to 0, the distribution is approximately symmetrical, although technically it's slightly right-skewed.

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Answer:

a) As = 0.67 right skewness

b) As = -0.75 left skewness

c) As = 0 ( Symmetric )

d) As = 0.1 ( slightly unsimmetric ) right skewness

Step-by-step explanation:

We will use the formula

As = skewness coefficient

μ = mean of distribution

Μ = median of distribution

And Pearson formula : As = ( μ - Μ) / σ

a) As = ( 10- 8 ) /3 =2/3 = 0.67

The distribution is right-skewness (positive skewness)

b) As = ( 42 - 45 ) / 4 = -3/4 = -0.75

The distribution is left skewness (negative skewness)

c) As = ( 18.6 - 18.6 )/ 1.5 = 0

The curve of the distribution is is symmetric

d) As = ( 98 - 97.6 ) / 4 = 0.4/4 = 0.1

The distribution is right skewness (slightly unsimmetric)

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