Skew in data
Name:
Date:
Class:
A
Quick Questions
Shade in the A or B circle for each question.
1. A data set has a long tail stretching to the high (right) side. What type of skew is this?
2. A distribution has most values high, with a few very low values forming a long tail on the left. What is its skew?
3. In a positively skewed data set, where is the mean compared with the median?
4. In a negatively skewed data set, where is the mean compared with the median?
5. Student house prices: most are $600,000 to $800,000 but a few are over $5 million. Which skew is likely?
B
Match the Pairs
Draw a line connecting each item on the left to its match on the right.
| Left column | Right column | |
|---|---|---|
| 1=SKEW(B2:B30) | ASKEW needs a range of values. A single cell cannot show how the whole data set is lopsided. | |
| 2=AVERAGE(B2:B30)>MEDIAN(B2:B30) | BCalculates a number showing how lopsided the data is: above 0 means positive skew, below 0 means negative skew | |
| 3Positive skew: a long tail to the high side, so the mean is greater than the median | C=IF(AVERAGE(C2:C40)>MEDIAN(C2:C40),"Positive skew","Not positive skew") | |
| 4Negative skew: a long tail to the low side, so the SKEW value is below zero | DReturns TRUE when the mean is pulled above the median, a sign of positive skew | |
| 5=SKEW(B2) | EA positive SKEW value means positive skew (a long tail to the high side). Only a negative value means negative skew. | |
| 6A SKEW value of 1.4 means negative skew, because the tail is long. | F=IF(SKEW(C2:C40)<0,"Negative skew","Not negative skew") |
C
Definitions
skew
D
Fill in the Blanks
Complete each line of code by filling in the missing parts.
1.
=____(B2:B30)
2.
If mean > median, skew is ________
3.
=AVERAGE(B2:B30)-______(B2:B30)
4.
=IF(SKEW(B2:B30)<_,"Negative","Positive")
5.
Long tail to the low side: ________ skew
E
Spot the Error
Shade in the letter of the line that contains an error.
Question 1
A
Mean: =AVERAGE(B2:B30)
B
Median: =MODE(B2:B30)
C
Skew: =SKEW(B2:B30)
Question 2
A
skew ← SKEW(B2:B30)
B
IF skew < 0 THEN
C
OUTPUT "Positive skew"
Question 3
A
mean ← AVERAGE(B2:B30)
B
median ← MEDIAN(B2:B30)
C
IF mean < median THEN
D
OUTPUT "Positive skew"
Question 4
A
mean ← 42
B
median ← 55
C
IF mean > median THEN
D
OUTPUT "Negative skew"
Question 5
A
// Incomes: a few very high
B
mean ← AVERAGE(B2:B30)
C
median ← MEDIAN(B2:B30)
D
OUTPUT "Mean is below median"
Answer Key
Skew in data
Section A: Quick Questions
Q1
A — Positive skew
Q2
B — Negative skew
Q3
B — The mean is greater than the median
Q4
A — The mean is less than the median
Q5
A — Positive skew
Section B: Match the Pairs
Q1
=SKEW(B2:B30) → Calculates a number showing how lopsided the data is: above 0 means positive skew, below 0 means negative skew
Q2
=AVERAGE(B2:B30)>MEDIAN(B2:B30) → Returns TRUE when the mean is pulled above the median, a sign of positive skew
Q3
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")
Q4
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")
Q5
=SKEW(B2) → SKEW needs a range of values. A single cell cannot show how the whole data set is lopsided.
Q6
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.
Section C: Definitions
Q1
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.Section D: Fill in the Blanks
Q1
=SKEW(B2:B30)Q2
If mean > median, skew is positiveQ3
=AVERAGE(B2:B30)-MEDIAN(B2:B30)Q4
=IF(SKEW(B2:B30)<0,"Negative","Positive")Q5
Long tail to the low side: negative skewSection E: Spot the Error
Q1
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.
Q2
B — A positive SKEW value means positive skew. The test should be skew > 0. skew < 0 would match negative skew instead.
Q3
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.
Q4
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.
Q5
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.