← VCE Data Analytics U4O1

Range as MAX minus MIN

Range is the largest value minus the smallest. It shows how spread out data is, but one outlier can stretch it. Not the same as a cell range like B2:B30.

Part of: VCE Data Analytics - U4O1 - Development and Evaluation — Module 26, ACARA Digital Technologies Years 7–8 — Analysing and Visualising Data — Module 18

Understanding Range as MAX minus MIN in VCE Data Analytics U4O1

What it does: The formula subtracts the smallest value from the largest, so a bigger answer means the data is more spread out. In the marks sheet the highest Maths mark is 95 and the lowest is 49. The formula gives 95 - 49 = 46. Range = 95 - 52 = 43. The highest mark alone (95) is just the maximum, not the range. The range uses only the largest and smallest values, so a single outlier can stretch it a lot. B2:B30 is a cell range, which is just a group of cells. The range of a data set is a calculated value, MAX minus MIN.

Common mistakes: Range is the largest value minus the smallest. E2-E1 is MIN minus MAX, which gives a negative number (-46). It should be =E1-E2. The range is 95 - 49 = 46. Adding the two values gives 144, which is not the spread. Line 4 should read Range = 46.

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This module's key terms are also in a printable crossword (Modules 3–37) and word search (Modules 3–62).

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Learning
Duo
Which formula finds the range of the values in B2:B30?
=MAX(B2:B30)+MIN(B2:B30)=MAX(B2:B30)-MIN(B2:B30)
Matches
=MIN(B2:B9)-MAX(B2:B9)
↓
MIN and MAX are the wrong way round. Subtracting the largest from the smallest gives a negative number. The range must be MAX minus MIN.
Applying
Meanings
Term
=MAX(B2:B30)-MIN(B2:B30)
Meaning
Range is the largest value minus the smallest. It shows how spread out data is, but one outlier can stretch it. Not the same as a cell range like B2:B30.
Practice
=MAX(B2:B9)-MIN(B2:B9)
Testing
Gaps
=(B2:B30)-MIN(B2:B30)
Check Answer
Spots
2E2: =MIN(B2:B9)
3E3: =E2-E1

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Quick Questions

1. Which formula finds the range of the values in B2:B30?
A. =MAX(B2:B30)-MIN(B2:B30) ✓
B. =MAX(B2:B30)+MIN(B2:B30)
Range is the largest value minus the smallest, so you subtract MIN from MAX. Adding them does not measure spread.
2. Maths marks are 52, 65, 77, 88 and 95. What is the range?
A. 43 ✓
B. 95
Range = 95 - 52 = 43. The highest mark alone (95) is just the maximum, not the range.
3. What does the range of a data set tell you?
A. The typical middle value
B. How spread out the values are ✓
Range measures spread from smallest to largest. The mean and median describe the centre.
4. Daily rain is 0, 2, 0, 14, 22, 5, 0 mm. Which statement is true?
A. The range is 14 mm
B. The range is 22 mm ✓
The largest value is 22 and the smallest is 0, so the range is 22 - 0 = 22 mm.
5. A class has marks mostly between 60 and 75, then one student scores 5. What happens to the range?
A. It gets much larger because of the outlier ✓
B. It stays about the same
The range uses only the largest and smallest values, so a single outlier can stretch it a lot.

Match the Pairs

=MAX(B2:B30)-MIN(B2:B30) → Calculates the range of the data: the largest value minus the smallest value in B2:B30
=MAX(C2:C9)-MIN(C2:C9) → Gives the spread between the highest and lowest values in C2:C9
Range is a measure of spread: how far apart the biggest and smallest values are → =MAX(B2:B9)-MIN(B2:B9)
For the Maths marks (49 to 95), the range is 46 because 95 - 49 = 46 → =MAX(B2:B9)-MIN(B2:B9)
=MIN(B2:B9)-MAX(B2:B9) → MIN and MAX are the wrong way round. Subtracting the largest from the smallest gives a negative number. The range must be MAX minus MIN.
=MAX(B2:B9)+MIN(B2:B9) → The formula adds MAX and MIN instead of subtracting. Adding gives a total, not the spread of the data.

Key Term

=MAX(B2:B30)-MIN(B2:B30)
Range is the largest value minus the smallest. It shows how spread out data is, but one outlier can stretch it. Not the same as a cell range like B2:B30.

Fill in the Blanks

1. =MAX(B2:B30)-MIN(B2:B30)
Hint: Type the function that finds the largest value in the range.
2. =MAX(B2:B30)-MIN(B2:B30)
Hint: Type the operator that subtracts the smallest value from the largest to find the range.
3. =MAX(D2:D8)-MIN(D2:D8)
Hint: Type the function that finds the smallest value, so the formula gives the range of the rainfall column.
4. =MAX(C2:C9)-MIN(C2:C9)
Hint: Type the same cell range that MAX uses, so both functions look at the same data.
5. =MAX(B2:B30)-MIN(B2:B30)
Hint: Type the symbol that every spreadsheet formula must start with.

Spot the Error

Question 1
A E1: =MAX(B2:B9)
B E2: =MIN(B2:B9)
C E3: =E2-E1
Line C — Range is the largest value minus the smallest. E2-E1 is MIN minus MAX, which gives a negative number (-46). It should be =E1-E2.
Question 2
A Range of Maths marks
B Max is 95, min is 49
C Range = 95 - 49
D Range = 144
Line D — The range is 95 - 49 = 46. Adding the two values gives 144, which is not the spread. Line 4 should read Range = 46.
Question 3
A F2: =MAX(C2:C9)+MIN(C2:C9)
B Max English 89, min 58
C Range is 89 - 58 = 31
Line A — Range subtracts the smallest value from the largest. The + adds them (147). It should be =MAX(C2:C9)-MIN(C2:C9).
Question 4
A Weather: daily max temps
B =MAX(B2:B8)-MAX(B2:B8)
C Highest 31, lowest 19
D Range is 12 degrees
Line B — Subtracting MAX from MAX always gives 0. The formula needs MIN for the smallest value: =MAX(B2:B8)-MIN(B2:B8).
Question 5
A Marks: 70, 72, 75, 74, 73
B Range is 75 - 70 = 5
C Add 20: range stays at 5
D One outlier stretches range
Line C — Adding an outlier of 20 makes the smallest value 20, so the range becomes 75 - 20 = 55. The range does not stay at 5, because it is affected by outliers.

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