Comparing mean and median

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Quick Questions

Shade in the A or B circle for each question.

1. A class's test scores are 60, 62, 65, 68 and 70. One student's score of 5 is added. Which statistic moves more?

A The median

B The mean

2. Five house prices in a suburb are $600k, $620k, $640k, $650k and $5,000k. Which value is the fairer typical price?

A The median

B The mean

3. The mean is much higher than the median. What does this suggest about the data?

A It is skewed by some very high values

B It is perfectly symmetrical

4. Which spreadsheet formulas let you check both measures of a typical value for the data in B2:B30?

A =AVERAGE(B2:B30) and =MEDIAN(B2:B30)

B =MEAN(B2:B30) and =MIDDLE(B2:B30)

5. The mean and median of a data set are almost the same. What is the most likely conclusion?

A There must be a very large outlier

B There are no strong outliers and the data is not very skewed

Match the Pairs

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

Left column		Right column
1=AVERAGE(B2:B20)		AMEDIAN barely changes when an outlier is added. It is AVERAGE (the mean) that gets dragged towards the outlier.
2=MEDIAN(B2:B20)		BAVERAGE = 950000, MEDIAN = 620000
3Check for skew by putting the mean and median side by side in two cells		C=AVERAGE(B2:B20) and =MEDIAN(B2:B20)
4With one huge house price in the list, the mean is much higher than the median		DThe mean is much higher than the median, which means the data is skewed. The median is the fairer typical value to report.
5Mean = 48, Median = 20, so report the mean as the typical value		EFinds the middle value, which barely moves when an outlier is present
6=MEDIAN(B2:B20) changes a lot if one salary is huge		FFinds the mean, which is pulled towards any outlier in the data

Definitions

mean vs median

Fill in the Blanks

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

=______(B2:B20)

=_______(B2:B20)

=AVERAGE(B2:B9)_MEDIAN(B2:B9)

=IF(AVERAGE(B2:B9)>______(B2:B9),"Skewed","")

D1: =AVERAGE(B2:B9) D2: =MEDIAN(B2:B9) D3: =IF(D1>__,"Skewed up","Not skewed")

Spot the Error

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

Question 1

A B2:B6 = 40, 42, 45, 47, 300

B D1: =AVERAGE(B2:B6)

C D2: =MEDIUM(B2:B6)

D D1 is pulled up by the 300

Question 2

A Salaries in B2:B7

B Mean: =AVERAGE(B2:B7)

C Median: =MEDIAN(B2:B7

D Big gap, so data is skewed

Question 3

A Data: 10, 12, 13, 14, 90

B Mean is 13, pulled up by 90

C Median is 13, the middle value

D Median is fairer to report

Question 4

A Data in A2:A8

B B1: AVERAGE(A2:A8)

C B2: =MEDIAN(A2:A8)

D If B1 is far from B2, skewed

Question 5

A Data: 3, 4, 5, 6, 7

B Mean = 5, Median = 5

C Similar, so it is skewed

D Either value is fine to report

Answer Key

Comparing mean and median

Section A: Quick Questions

B — The mean

A — The median

A — It is skewed by some very high values

A — =AVERAGE(B2:B30) and =MEDIAN(B2:B30)

B — There are no strong outliers and the data is not very skewed

Section B: Match the Pairs

=AVERAGE(B2:B20) → Finds the mean, which is pulled towards any outlier in the data

=MEDIAN(B2:B20) → Finds the middle value, which barely moves when an outlier is present

Check for skew by putting the mean and median side by side in two cells → =AVERAGE(B2:B20) and =MEDIAN(B2:B20)

With one huge house price in the list, the mean is much higher than the median → AVERAGE = 950000, MEDIAN = 620000

Mean = 48, Median = 20, so report the mean as the typical value → The mean is much higher than the median, which means the data is skewed. The median is the fairer typical value to report.

=MEDIAN(B2:B20) changes a lot if one salary is huge → MEDIAN barely changes when an outlier is added. It is AVERAGE (the mean) that gets dragged towards the outlier.

Section C: Definitions

mean vs median — An outlier drags the mean towards it but barely moves the median. If the two differ a lot, the data is skewed, so the median is usually the fairer typical value to report.

Section D: Fill in the Blanks

=MEDIAN(B2:B20)

=AVERAGE(B2:B20)

=AVERAGE(B2:B9)-MEDIAN(B2:B9)

=IF(AVERAGE(B2:B9)>MEDIAN(B2:B9),"Skewed","")

D1: =AVERAGE(B2:B9)
D2: =MEDIAN(B2:B9)
D3: =IF(D1>D2,"Skewed up","Not skewed")

Section E: Spot the Error

C — MEDIUM is not a spreadsheet function. The function that finds the middle value is MEDIAN, so the line should be D2: =MEDIAN(B2:B6).

C — The formula is missing its closing bracket. It should be =MEDIAN(B2:B7).

B — The mean is (10+12+13+14+90) / 5 = 27.8, not 13. 13 is the median. The outlier 90 drags the mean up to 27.8.

B — A formula must start with =, otherwise the spreadsheet treats it as plain text. It should be B1: =AVERAGE(A2:A8).

C — The mean and median are both 5. When they are similar the data is not skewed, so the line should say the data is not skewed.