A measure of how asymmetric a probability distribution is around its mean โ 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 (xiโโโxiโ). The new skewness equals what?
Example 3
hard
Compute the sample skewness of the data {1,2,3,4,10}. Use skew=(nโ1)(nโ2)nโโ(sxiโโxหโ)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 = +0.9. Where does the longer tail point?
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 Sk2โ=s3(xหโmedian)โ. A class has xห=72, median =78, s=6. Compute Sk2โ.Class: mean = 72, median = 78, s = 6. Compute Pearson's Skโ.
Example 8
medium
A right-skewed dataset has every value negated (xiโโโxiโ). 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 ฮป has theoretical skewness 2. Why does this number not depend on ฮป?
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 โ2.4. Briefly describe the shape.Sample skewness = โ2.4. 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 = 60, Median = 50. What type of skew?
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?