← VCE Data Analytics U3O1

Range of a data set

The range is the largest value minus the smallest value. It measures spread, and one outlier can make it much bigger.

Part of: VCE Data Analytics - U3O1 - Data Analytics — Module 83, ACARA Digital Technologies Years 9–10 — Analysing and Visualising Data — Module 16

Understanding Range of a data set in VCE Data Analytics U3O1

What it does: The Maths marks are in B2:B9, so the formula subtracts the MIN of that column from its MAX. The weather sheet has Max temperatures in B2:B8. Subtracting MIN from MAX gives the range of those values. The range is the largest value minus the smallest value, so you subtract MIN from MAX. Range = 95 - 49 = 46. Adding the two values (144) is a common mistake. The range is a measure of spread. Mean and median describe the centre. Both MAX and MIN must use the same column of data. C2:C8 holds the Min temperatures. The range depends entirely on the two extreme values, so outliers change it.

Common mistakes: E3 should hold the smallest value, so it needs MIN(B2:B30). With MAX in both cells, E2-E3 would always be 0 instead of the range. The range is the largest value minus the smallest value. The formula must be =MAX(C2:C9)-MIN(C2:C9). The broken version gives a negative number.

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This module's key terms are also in a printable crossword (Modules 50–91) and word search (Modules 17–91).

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Learning
Duo
Which formula correctly 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. This subtracts the largest value from the smallest, so the range comes out negative.
Applying
Meanings
Term
=MAX(B2:B30)-MIN(B2:B30)
Meaning
The range is the largest value minus the smallest value. It measures spread, and one outlier can make it much bigger.
Practice
=MAX(B2:B9)-MIN(B2:B9)
Testing
Gaps
=(B2:B30)-MIN(B2:B30)
Check Answer
Spots
1E2: =MAX(B2:B30)
2E3: =MAX(B2:B30)

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Quick Questions

1. Which formula correctly finds the range of the values in B2:B30?
A. =MAX(B2:B30)-MIN(B2:B30) ✓
B. =MAX(B2:B30)+MIN(B2:B30)
The range is the largest value minus the smallest value, so you subtract MIN from MAX.
2. A set of marks has a highest mark of 95 and a lowest mark of 49. What is the range?
A. 46 ✓
B. 144
Range = 95 - 49 = 46. Adding the two values (144) is a common mistake.
3. What does the range tell you about a data set?
A. The typical middle value
B. How spread out the values are ✓
The range is a measure of spread. Mean and median describe the centre.
4. Using the weather sheet, Max temperatures are in B2:B8 (lowest 19, highest 31). Which formula gives the range of Max temperatures?
A. =MAX(B2:B8)-MIN(C2:C8)
B. =MAX(B2:B8)-MIN(B2:B8) ✓
Both MAX and MIN must use the same column of data. C2:C8 holds the Min temperatures.
5. Most students scored between 60 and 80, but one student scored 5. What happens to the range?
A. It gets much bigger because of the outlier ✓
B. It stays about the same
The range uses the smallest and largest values, so a single outlier can stretch it a lot.

Match the Pairs

=MAX(B2:B9)-MIN(B2:B9) → Finds the range of the values in B2:B9 by subtracting the smallest value from the largest value
=MAX(D2:D8)-MIN(D2:D8) → Shows how spread out the values in D2:D8 are, from the lowest to the highest
The range of the Maths marks is the highest mark minus the lowest mark → =MAX(B2:B9)-MIN(B2:B9)
The range of the daily maximum temperatures is the hottest day minus the coolest of the maximums → =MAX(B2:B8)-MIN(B2:B8)
=MIN(B2:B9)-MAX(B2:B9) → MIN and MAX are the wrong way round. This subtracts the largest value from the smallest, so the range comes out negative.
=MAX(B2:B9)+MIN(B2:B9) → The formula adds the values instead of subtracting. This gives the sum of the highest and lowest values, not the range.

Key Term

=MAX(B2:B30)-MIN(B2:B30)
The range is the largest value minus the smallest value. It measures spread, and one outlier can make it much bigger.

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 arithmetic operator that works out the range from the largest and smallest values.
3. =MAX(C2:C9)-MIN(C2:C9)
Hint: Type the function that finds the smallest value in the column.
4. =MAX(B2:B8)-MIN(B2:B8)
Hint: Type the same cell range that the MAX function uses, so both look at the same data.
5. =MAX(B2:B9)-MIN(B2:B9)
Hint: Type the cell range holding the Maths marks, from the first student to the last.

Spot the Error

Question 1
A E2: =MAX(B2:B30)
B E3: =MAX(B2:B30)
C E4: =E2-E3
Line B — E3 should hold the smallest value, so it needs MIN(B2:B30). With MAX in both cells, E2-E3 would always be 0 instead of the range.
Question 2
A =MIN(C2:C9)-MAX(C2:C9)
B Range = highest - lowest
C Bigger range = more spread
Line A — The range is the largest value minus the smallest value. The formula must be =MAX(C2:C9)-MIN(C2:C9). The broken version gives a negative number.
Question 3
A highest ← MAX(marks)
B lowest ← AVERAGE(marks)
C range ← highest - lowest
Line B — The range needs the smallest value, so lowest must be MIN(marks). AVERAGE gives the mean, which is not the lowest value.
Question 4
A Marks: 40, 55, 60, 95
B Highest = 95
C Lowest = 40
D Range = 95 + 40 = 55
Line D — The range is the highest value minus the lowest value, so it is 95 - 40 = 55. Adding them (95 + 40) is wrong and does not equal 55.
Question 5
A Set A: 50, 52, 55, 58
B Set B: 50, 52, 55, 158
C Range of B = 158 - 50 = 98
D An outlier makes range bigger
Line C — 158 - 50 is 108, not 98. The outlier 158 makes the range of Set B much larger than the range of Set A, which is 8.

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