← VCE Spreadsheets, SQL & Visualisation

Interpreting standard deviation

A measure of how spread out values are around the mean. A small value means the data is clustered close to the mean. A large value means it is widely spread. It uses the same units as the data.

Part of: VCE Applied Computing - U1O1 - Data analysis — Module 23, VCE Data Analytics - U3O1 - Data Analytics — Module 87, VCE Data Analytics - U4O1 - Development and Evaluation — Module 28, ACARA Digital Technologies Years 9–10 — Analysing and Visualising Data — Module 18

Understanding Interpreting standard deviation in VCE Spreadsheets, SQL & Visualisation

What it does: With the same mean, the group with the smaller standard deviation has values closer together, so Class A is more clustered and Class B is more spread out. Subtract 5 from the mean (40 - 5 = 35) and add 5 to the mean (40 + 5 = 45). Most values usually fall in this range.

Common mistakes: A small standard deviation means the marks are clustered close to the mean, not widely spread. It should say 'Small SD = marks clustered'. Group A has the smaller SD (3), so its values are closer to the mean. Group A is more consistent, not Group B.

Class: _____________________  ·  Name: _____________________  ·  Date: _________

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This module's key terms are also in a printable crossword (Modules 21–34) and word search (Modules 4–34).

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Learning
Duo
Class A and Class B both have a mean test score of 70. Class A has a standard deviation of 3 and Class B has a standard deviation of 15. Which class has scores that are more clustered around the mean?
Class B, because its standard deviation is largerClass A, because its standard deviation is smaller
Matches
Team A: mean = 50, SD = 2 Team B: mean = 50, SD = 9 Team A is more spread out.
↓
Team A has the smaller SD, so its values are more clustered, not more spread out. Team B is the more spread out group.
Applying
Meanings
Term
standard deviation
Meaning
A measure of how spread out values are around the mean. A small value means the data is clustered close to the mean. A large value means it is widely spread. It uses the same units as the data.
Practice
=AVERAGE(B2:B21)
Testing
Gaps
=(B2:B11)
Check Answer
Spots
3SD: =STDEV.S(A2:A9)
4Small SD = marks widely spread

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Quick Questions

1. Class A and Class B both have a mean test score of 70. Class A has a standard deviation of 3 and Class B has a standard deviation of 15. Which class has scores that are more clustered around the mean?
A. Class B, because its standard deviation is larger
B. Class A, because its standard deviation is smaller ✓
A small standard deviation means the values are clustered close to the mean. Class B's scores are more spread out.
2. A large standard deviation tells you that the values are...
A. Widely spread around the mean ✓
B. Clustered close to the mean
The larger the standard deviation, the further the values tend to sit from the mean.
3. Two shops both have a mean of 50 customers per day. Shop X has a standard deviation of 2 and Shop Y has a standard deviation of 20. Which statement is correct?
A. Shop Y's daily customer numbers vary much more ✓
B. Shop X's daily customer numbers vary much more
The same mean can hide very different spreads. Only the standard deviation shows how much the values vary.
4. A dataset of heights is measured in centimetres and has a standard deviation of 8. What unit does the standard deviation use?
A. Percent, because it measures spread
B. Centimetres, the same unit as the data ✓
Standard deviation is in the same units as the original data, so a spread of 8 here means 8 cm.
5. A set of data has a mean of 40 and a standard deviation of 5. What is the range for mean plus or minus one standard deviation?
A. 35 to 45 ✓
B. 40 to 45
Subtract 5 from the mean (40 - 5 = 35) and add 5 to the mean (40 + 5 = 45). Most values usually fall in this range.

Match the Pairs

=STDEV.S(B2:B31) → Calculates the sample standard deviation of the values in B2:B31, which shows how spread out they are around the mean
=AVERAGE(B2:B31)-STDEV.S(B2:B31) → Finds the lower end of the typical range: the mean minus one standard deviation
Two classes both have a mean of 70, but Class A has a standard deviation of 3 and Class B has 15. Class A marks are more clustered → Class A: mean = 70, SD = 3 Class B: mean = 70, SD = 15
Standard deviation uses the same units as the data, so a SD of 4 for waiting times in minutes means 4 minutes → Mean wait = 12 min, SD = 4 min
Team A: mean = 50, SD = 2 Team B: mean = 50, SD = 9 Team A is more spread out. → Team A has the smaller SD, so its values are more clustered, not more spread out. Team B is the more spread out group.
Mean = 40 kg, SD = 5 kg Most values are between 35 and 50 kg → Mean plus or minus one SD is 40 - 5 to 40 + 5, which is 35 to 45 kg, not 35 to 50 kg.

Key Term

standard deviation
A measure of how spread out values are around the mean. A small value means the data is clustered close to the mean. A large value means it is widely spread. It uses the same units as the data.

Fill in the Blanks

1. =STDEV.S(B2:B11)
Hint: Type the function that measures how spread out the values are around the mean.
2. =AVERAGE(B2:B11)-STDEV.S(B2:B11)
Hint: Type the operator that finds one standard deviation below the mean.
3. =AVERAGE(B2:B11)+STDEV.S(B2:B11)
Hint: Type the function for the spread that is added to the mean to find the upper limit.
4. =IF(STDEV.S(B2:B6)<STDEV.S(C2:C6),"A","B")
Hint: Type the comparison operator that checks if group A's spread is smaller than group B's, so A is more consistent.
5. =AVERAGE(B2:B11)-STDEV.S(B2:B11) =AVERAGE(B2:B11)+STDEV.S(B2:B11)
Hint: Type the function that gives the centre of the data, which the standard deviation is added to or taken from.

Spot the Error

Question 1
A A2:A9 holds quiz marks
B Mean: =AVERAGE(A2:A9)
C SD: =STDEV.S(A2:A9)
D Small SD = marks widely spread
Line D — A small standard deviation means the marks are clustered close to the mean, not widely spread. It should say 'Small SD = marks clustered'.
Question 2
A Group A mean = 70, SD = 3
B Group B mean = 70, SD = 15
C Group B is more consistent
D Same mean, different spread
Line C — Group A has the smaller SD (3), so its values are closer to the mean. Group A is more consistent, not Group B.
Question 3
A Test marks: mean = 62 marks
B SD = 8 marks squared
C SD uses the same units: marks
Line B — Standard deviation uses the same units as the data, so it is in marks. 'Marks squared' would be the variance. It should be 'SD = 8 marks'.
Question 4
A Mean = 50, SD = 10
B Mean - 1 SD = 40
C Mean + 1 SD = 60
D Range within 1 SD: 40 to 70
Line D — Mean plus 1 SD is 50 + 10 = 60, so the range within one SD of the mean is 40 to 60, not 40 to 70.
Question 5
A SD: =AVERAGE(B2:B21)
B Result: 4 minutes
C Times typically vary by 4 min
Line A — AVERAGE calculates the mean, not the standard deviation. The SD is found with =STDEV.S(B2:B21).

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