← VCE Spreadsheets, SQL & Visualisation

Comparing mean and 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.

Part of: VCE Applied Computing - U1O1 - Data analysis — Module 19, VCE Data Analytics - U3O1 - Data Analytics — Module 82, VCE Data Analytics - U4O1 - Development and Evaluation — Module 30, ACARA Digital Technologies Years 7–8 — Analysing and Visualising Data — Module 33, ACARA Digital Technologies Years 9–10 — Acquiring and Validating Data — Module 113, ACARA Digital Technologies Years 9–10 — Analysing and Visualising Data — Module 15

Understanding Comparing mean and median in VCE Spreadsheets, SQL & Visualisation

What it does: If these two results are far apart, an outlier or skew is probably affecting the data, so the median may be the fairer typical value. The $5,000k mansion pulls the mean up. The median stays close to most of the prices, so it is fairer to report. Spreadsheets use AVERAGE for the mean and MEDIAN for the middle value. MEAN() and MIDDLE() are not the usual functions. When the two values are close, no extreme values are pulling the mean away from the middle. AVERAGE adds up all the values and divides by how many there are, so one extreme value can drag the result up or down.

Common mistakes: MEDIUM is not a spreadsheet function. The function that finds the middle value is MEDIAN, so the line should be D2: =MEDIAN(B2:B6). The formula is missing its closing bracket. It should be =MEDIAN(B2:B7).

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This module's key terms are also in a printable crossword (Modules 4–20) and word search (Modules 4–34).

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Learning
Duo
A class's test scores are 60, 62, 65, 68 and 70. One student's score of 5 is added. Which statistic moves more?
The meanThe median
Matches
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.
Applying
Meanings
Term
mean vs median
Meaning
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.
Practice
=AVERAGE(B2:B11)
Testing
Gaps
=(B2:B20)
Check Answer
Spots
2D1: =AVERAGE(B2:B6)
3D2: =MEDIUM(B2:B6)

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Quick Questions

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 ✓
The outlier of 5 drags the mean down a lot, but the median only shifts to the next middle value.
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
The $5,000k mansion pulls the mean up. The median stays close to most of the prices, so it is fairer to report.
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
A mean well above the median means high outliers are pulling the mean up. Symmetrical data has a mean and median that are close.
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)
Spreadsheets use AVERAGE for the mean and MEDIAN for the middle value. MEAN() and MIDDLE() are not the usual functions.
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 ✓
When the two values are close, no extreme values are pulling the mean away from the middle.

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.

Key Term

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.

Fill in the Blanks

1. =MEDIAN(B2:B20)
Hint: Type the function that returns the middle value, which an outlier barely moves.
2. =AVERAGE(B2:B20)
Hint: Type the function that calculates the mean, which an outlier pulls towards it.
3. =AVERAGE(B2:B9)-MEDIAN(B2:B9)
Hint: Type the operator that finds the difference between the mean and the median.
4. =IF(AVERAGE(B2:B9)>MEDIAN(B2:B9),"Skewed","")
Hint: Type the function whose result is compared with the mean to spot skew.
5. D1: =AVERAGE(B2:B9) D2: =MEDIAN(B2:B9) D3: =IF(D1>D2,"Skewed up","Not skewed")
Hint: Type the cell reference that holds the median so it can be compared with the mean in D1.

Spot the 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
Line 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).
Question 2
A Salaries in B2:B7
B Mean: =AVERAGE(B2:B7)
C Median: =MEDIAN(B2:B7
D Big gap, so data is skewed
Line C — The formula is missing its closing bracket. It should be =MEDIAN(B2:B7).
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
Line 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.
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
Line B — A formula must start with =, otherwise the spreadsheet treats it as plain text. It should be B1: =AVERAGE(A2:A8).
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
Line 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.

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