Skew: positive and negative

Name:

Date:

Class:

Quick Questions

Shade in the A or B circle for each question.

1. A data set has a long tail stretching to the right (high values). What is this called?

A Negative (left) skew

B Positive (right) skew

2. A data set has a long tail stretching to the left (low values). What is this called?

A Positive (right) skew

B Negative (left) skew

3. In positively skewed data, which statement is usually true?

A The mean is greater than the median

B The mean is less than the median

4. In negatively skewed data, which statement is usually true?

A The mean is less than the median

B The mean is greater than the median

5. House prices in a suburb: most are $600k to $800k, but a few are over $5 million. Which skew is this?

A Positive skew, because a few very high values form a right tail

B Negative skew, because the few very high values pull the data down

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
1Mean > Median		AA sign of negative (left) skew: a long tail of low values pulls the mean below the median
2Mean < Median		BSkew is named after the direction of the tail. A left tail is negative skew, not positive skew.
3House prices have a few very expensive sales on the right, so the data is positively skewed and the mean is higher than the median		CA sign of positive (right) skew: a long tail of high values pulls the mean above the median
4For skewed data, the median is usually the better measure of the typical value because it stays nearer the bulk of the data		D=AVERAGE(B2:B50)>MEDIAN(B2:B50)
5The tail points left, so the data is positively skewed		EIn right (positive) skew the tail pulls the mean up, so the mean is above the median, not below it.
6Data is skewed right, so the mean is below the median		F=MEDIAN(B2:B50)

Definitions

skew

Fill in the Blanks

Complete each line of code by filling in the missing parts.

=AVERAGE(A2:A40)>______(A2:A40)

IF mean _ median THEN OUTPUT "Positive skew" END IF

IF mean _ median THEN OUTPUT "Negative skew" END IF

avg = statistics.____(marks) mid = statistics.median(marks) print(avg > mid)

IF skewed THEN centre ← ______ END IF

Spot the Error

Shade in the letter of the line that contains an error.

Question 1

A data = [2, 3, 3, 4, 40]

B mean = sum(data) / len(data)

C median = 3

D if mean < median:

E print("positive skew")

Question 2

A import statistic

B data = [1, 50, 55, 58, 60]

C mean = statistics.mean(data)

D median = statistics.median(data)

E print(mean < median)

Question 3

A incomes = [30, 32, 35, 38, 150]

B mean = sum(incomes) / 5

C median = sorted(incomes)[4]

D print(mean, median)

Question 4

A data = [5, 6, 6, 7, 8, 30]

B tail = "left"

C skew = "positive"

D print(tail, skew)

Question 5

A mean = 72

B median = 80

C skew = "positive"

D print("Skew:", skew)

Answer Key

Skew: positive and negative

Section A: Quick Questions

B — Positive (right) skew

B — Negative (left) skew

A — The mean is greater than the median

A — The mean is less than the median

A — Positive skew, because a few very high values form a right tail

Section B: Match the Pairs

Mean > Median → A sign of positive (right) skew: a long tail of high values pulls the mean above the median

Mean < Median → A sign of negative (left) skew: a long tail of low values pulls the mean below the median

House prices have a few very expensive sales on the right, so the data is positively skewed and the mean is higher than the median → =AVERAGE(B2:B50)>MEDIAN(B2:B50)

For skewed data, the median is usually the better measure of the typical value because it stays nearer the bulk of the data → =MEDIAN(B2:B50)

The tail points left, so the data is positively skewed → Skew is named after the direction of the tail. A left tail is negative skew, not positive skew.

Data is skewed right, so the mean is below the median → In right (positive) skew the tail pulls the mean up, so the mean is above the median, not below it.

Section C: Definitions

skew — Data with a longer tail on one side. The tail pulls the mean its way: a right tail is positive skew, a left tail is negative skew, and the median stays nearer the bulk.

Section D: Fill in the Blanks

=AVERAGE(A2:A40)>MEDIAN(A2:A40)

IF mean > median THEN
  OUTPUT "Positive skew"
END IF

IF mean < median THEN
  OUTPUT "Negative skew"
END IF

avg = statistics.mean(marks)
mid = statistics.median(marks)
print(avg > mid)

IF skewed THEN
  centre ← median
END IF

Section E: Spot the Error

D — A long right tail pulls the mean above the median, so positive skew is when mean > median. The condition should be if mean > median:.

A — The module is called statistics, with an s. Without it, statistics.mean() and statistics.median() fail. It should be import statistics.

C — With 5 sorted values the median is the middle one, at index 2. Index 4 is the largest value (the outlier), not the median. It should be [2].

B — The long tail stretches towards the large value 30, so the tail is on the right. A right tail means positive skew. It should be tail = "right".

C — The mean (72) is below the median (80), so a left tail is pulling the mean down. That is negative skew. It should be skew = "negative".