← VCE Data Analytics U3O1

Skew in data

Lopsidedness of a distribution: positive skew has a long tail to the high side, negative skew to the low side. The mean is pulled towards the tail, away from the median.

Part of: VCE Data Analytics - U3O1 - Data Analytics — Module 95

Understanding Skew in data in VCE Data Analytics U3O1

What it does: Comparing the mean with the median tests for positive skew, because a tail of high values pulls the mean up. The tail points to the low side, so the skew is negative. SKEW takes a range and returns a number. SKEWNESS is not a spreadsheet function. A negative SKEW value means negative skew. A positive value means positive skew. A value near 0 means roughly symmetrical. Skew describes the shape of many values, so the formula must use a range such as =SKEW(B2:B30).

Common mistakes: MODE finds the most common value, not the middle one. The median is found with =MEDIAN(B2:B30), which is what you compare with the mean to judge skew. A positive SKEW value means positive skew. The test should be skew > 0. skew < 0 would match negative skew instead.

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Free printable worksheet with full answer key — or add this module to a class and your students practise it interactively.

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This module's key terms are also in a printable crossword (Modules 94–128) and word search (Modules 94–148).

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Learning
Duo
A data set has a long tail stretching to the high (right) side. What type of skew is this?
Negative skewPositive skew
Matches
=SKEW(B2)
↓
SKEW needs a range of values. A single cell cannot show how the whole data set is lopsided.
Applying
Meanings
Term
skew
Meaning
Lopsidedness of a distribution: positive skew has a long tail to the high side, negative skew to the low side. The mean is pulled towards the tail, away from the median.
Practice
=AVERAGE(D2:D8)-MEDIAN(D2:D8)
Testing
Gaps
=(B2:B30)
Check Answer
Spots
1Mean: =AVERAGE(B2:B30)
2Median: =MODE(B2:B30)

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Quick Questions

1. A data set has a long tail stretching to the high (right) side. What type of skew is this?
A. Positive skew ✓
B. Negative skew
Skew is named after the direction of the long tail. A long tail to the high side is positive skew.
2. A distribution has most values high, with a few very low values forming a long tail on the left. What is its skew?
A. Positive skew
B. Negative skew ✓
The tail points to the low side, so the skew is negative.
3. In a positively skewed data set, where is the mean compared with the median?
A. The mean is less than the median
B. The mean is greater than the median ✓
A few very high values pull the mean up towards the tail, so the mean sits above the median.
4. In a negatively skewed data set, where is the mean compared with the median?
A. The mean is less than the median ✓
B. The mean is greater than the median
A few very low values drag the mean down towards the low tail, below the median.
5. Student house prices: most are $600,000 to $800,000 but a few are over $5 million. Which skew is likely?
A. Positive skew ✓
B. Negative skew
A few very high values make a long tail on the high side, which is positive skew.

Match the Pairs

=SKEW(B2:B30) → Calculates a number showing how lopsided the data is: above 0 means positive skew, below 0 means negative skew
=AVERAGE(B2:B30)>MEDIAN(B2:B30) → Returns TRUE when the mean is pulled above the median, a sign of positive skew
Positive skew: a long tail to the high side, so the mean is greater than the median → =IF(AVERAGE(C2:C40)>MEDIAN(C2:C40),"Positive skew","Not positive skew")
Negative skew: a long tail to the low side, so the SKEW value is below zero → =IF(SKEW(C2:C40)<0,"Negative skew","Not negative skew")
=SKEW(B2) → SKEW needs a range of values. A single cell cannot show how the whole data set is lopsided.
A SKEW value of 1.4 means negative skew, because the tail is long. → A positive SKEW value means positive skew (a long tail to the high side). Only a negative value means negative skew.

Key Term

skew
Lopsidedness of a distribution: positive skew has a long tail to the high side, negative skew to the low side. The mean is pulled towards the tail, away from the median.

Fill in the Blanks

1. =SKEW(B2:B30)
Hint: Type the spreadsheet function name that measures how lopsided a distribution is.
2. If mean > median, skew is positive
Hint: Type the kind of skew when the mean is pulled above the median by a long high tail.
3. =AVERAGE(B2:B30)-MEDIAN(B2:B30)
Hint: Type the function name for the middle value, to compare against the mean.
4. =IF(SKEW(B2:B30)<0,"Negative","Positive")
Hint: Type the SKEW value that separates negative skew from positive skew.
5. Long tail to the low side: negative skew
Hint: Type the kind of skew that has its tail stretching towards the low values.

Spot the Error

Question 1
A Mean: =AVERAGE(B2:B30)
B Median: =MODE(B2:B30)
C Skew: =SKEW(B2:B30)
Line B — MODE finds the most common value, not the middle one. The median is found with =MEDIAN(B2:B30), which is what you compare with the mean to judge skew.
Question 2
A skew ← SKEW(B2:B30)
B IF skew < 0 THEN
C OUTPUT "Positive skew"
Line B — A positive SKEW value means positive skew. The test should be skew > 0. skew < 0 would match negative skew instead.
Question 3
A mean ← AVERAGE(B2:B30)
B median ← MEDIAN(B2:B30)
C IF mean < median THEN
D OUTPUT "Positive skew"
Line C — In positive skew the long high tail pulls the mean above the median. The condition should be mean > median. mean < median points to negative skew.
Question 4
A mean ← 42
B median ← 55
C IF mean > median THEN
D OUTPUT "Negative skew"
Line C — Negative skew has a long low tail that drags the mean below the median. The test for negative skew is mean < median, not mean > median.
Question 5
A // Incomes: a few very high
B mean ← AVERAGE(B2:B30)
C median ← MEDIAN(B2:B30)
D OUTPUT "Mean is below median"
Line D — A few very high incomes make a long high tail (positive skew). The mean is pulled up towards the tail, so it is above the median, not below.

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