A measure of how asymmetric a probability distribution is around its mean — positive skew tails right, negative skew tails left.
A right-skewed distribution has a long tail to the right (a few very large values); left-skewed has a long tail to the left.
Showing a random 20 of 50 problems.
Example 1
easy
Is the sign of skewness determined by the direction of the tail or the side where most data sits?
Example 2
medium
A symmetric dataset has all its values negated (xi→−xi). The new skewness equals what?
Example 3
hard
Compute the sample skewness of the data {1,2,3,4,10}. Use skew=(n−1)(n−2)n∑(sxi−xˉ)3 and round to two decimals.Data: {1, 2, 3, 4, 10}. Compute the sample skewness.
Example 4
easy
Does the sign of the skewness tell you the direction of the longer tail?
Example 5
medium
A distribution has skewness +0.9. Where does the longer tail point, and how do mean and median compare?Skewness
Example 6
medium
A dataset has mean 25, median 30, mode 35. Describe the skew using the order of mean, median, and mode.Mean = 25, Median = 30, Mode = 35. Describe the skew.
Example 7
hard
Pearson's second skewness coefficient is Sk2=s3(xˉ−median). A class has xˉ=72, median =78, s=6. Compute Sk2.Class: mean
Example 8
medium
A right-skewed dataset has every value negated (xi→−xi). What kind of skew does the new dataset have?
Example 9
easy
Income data with a few billionaires typically has which skew?
Example 10
hard
A dataset of 100 salaries has skewness +3. A single $5M salary is removed. Most likely the new skewness is closer to which: +3, +1.5, or 0?
Example 11
challenge
An exponential distribution with rate λ has theoretical skewness 2. Why does this number not depend on λ?
Example 12
medium
Exam scores cluster near the top with a few low outliers. What skew, and how do mean and median compare?Scores cluster near the top with a few low outliers. What skew?
Example 13
medium
A sample skewness is reported as −2.4. Briefly describe the shape.Sample skewness = −2.4. Describe the shape.
Example 14
easy
A distribution with a long tail to the RIGHT has what type of skew?Which direction does the long tail point?
Example 15
challenge
A researcher reports a sample skewness of +0.05 for n=20 observations and concludes the population is right-skewed. Why is this conclusion premature?
Example 16
easy
The skewness of a perfectly normal distribution equals what value?
Example 17
easy
A distribution with a long tail to the LEFT has what type of skew?Which direction does the long tail point?
Example 18
easy
A histogram has a long thin tail stretching toward larger values on the right. What is its skew?What type of skew does this histogram show?
Example 19
medium
A data set has mean 60 and median 50. Describe its skew.Mean
Example 20
hard
A teacher claims, 'My class scored higher than the median, so I'm above average.' If scores are strongly right-skewed, why is this reasoning suspect?