Interpreting standard deviation

Name:

Date:

Class:

Quick Questions

Shade in the A or B circle for each question.

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

2. A large standard deviation tells you that the values are...

A Widely spread around the mean

B Clustered close to 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

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

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

Match the Pairs

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

Left column		Right column
1=STDEV.S(B2:B31)		AFinds the lower end of the typical range: the mean minus one standard deviation
2=AVERAGE(B2:B31)-STDEV.S(B2:B31)		BMean wait = 12 min, SD = 4 min
3Two 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		CTeam A has the smaller SD, so its values are more clustered, not more spread out. Team B is the more spread out group.
4Standard deviation uses the same units as the data, so a SD of 4 for waiting times in minutes means 4 minutes		DClass A: mean = 70, SD = 3 Class B: mean = 70, SD = 15
5Team A: mean = 50, SD = 2 Team B: mean = 50, SD = 9 Team A is more spread out.		EMean plus or minus one SD is 40 - 5 to 40 + 5, which is 35 to 45 kg, not 35 to 50 kg.
6Mean = 40 kg, SD = 5 kg Most values are between 35 and 50 kg		FCalculates the sample standard deviation of the values in B2:B31, which shows how spread out they are around the mean

Definitions

standard deviation

Fill in the Blanks

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

=_______(B2:B11)

=AVERAGE(B2:B11)_STDEV.S(B2:B11)

=AVERAGE(B2:B11)+_______(B2:B11)

=IF(STDEV.S(B2:B6)_STDEV.S(C2:C6),"A","B")

=AVERAGE(B2:B11)-STDEV.S(B2:B11) =_______(B2:B11)+STDEV.S(B2:B11)

Spot the Error

Shade in the letter of the line that contains an 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

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

Question 3

A Test marks: mean = 62 marks

B SD = 8 marks squared

C SD uses the same units: 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

Question 5

A SD: =AVERAGE(B2:B21)

B Result: 4 minutes

C Times typically vary by 4 min

Answer Key

Interpreting standard deviation

Section A: Quick Questions

B — Class A, because its standard deviation is smaller

A — Widely spread around the mean

A — Shop Y's daily customer numbers vary much more

B — Centimetres, the same unit as the data

A — 35 to 45

Section B: 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.

Section C: Definitions

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.

Section D: Fill in the Blanks

=STDEV.S(B2:B11)

=AVERAGE(B2:B11)-STDEV.S(B2:B11)

=AVERAGE(B2:B11)+STDEV.S(B2:B11)

=IF(STDEV.S(B2:B6)<STDEV.S(C2:C6),"A","B")

=AVERAGE(B2:B11)-STDEV.S(B2:B11)
=AVERAGE(B2:B11)+STDEV.S(B2:B11)

Section E: Spot the Error

D — A small standard deviation means the marks are clustered close to the mean, not widely spread. It should say 'Small SD = marks clustered'.

C — Group A has the smaller SD (3), so its values are closer to the mean. Group A is more consistent, not Group B.

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'.

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.

A — AVERAGE calculates the mean, not the standard deviation. The SD is found with =STDEV.S(B2:B21).