Standard Deviation

Question 1

What is “standard deviation?”

Answer 1

• Spread of data about the mean value.

Question 2

Why is standard deviation more useful than calculating the range of data? 3 main reasons!

Answer 2

1.) SD shows spread of data from the mean, whereas, range is only difference between the highest/ lowest value.
2.) SD reduces the effect of anomalies whereas, range includes anomalies.
3.) SD can be used to indicate whether a difference between results is significant.

Question 3

Why would standard deviation be useful for making a conclusion from data?

Answer 3

• Overlaps between SD, shows that there is likely to be significant difference between the mean values.
• No overlap between SD shows that it is likely there is NO significant difference between the mean values.

Question 4

Past paper 1 2023

Mean diameter of clear zone =
1.) 16.6, standard deviation is +/-2.4
2.) 13.4, standard deviation is +/-2.2
Use this information to consider whether the differences in means are liklely due to chance.
Explain using at least 1 calc.

Answer 4

• SD’s overlap so likely difference is due to chance.
• Calculations:
  16.6 +/- (2x2.4) =
  11.8 –> 21.4
  13.4 +/- (2x2.2) =
  9–> 17.8

Question 5

How do you work out the RANGE of values from standard deviation and mean, when standard deviations are +/-2 over 95% over data?

Answer 5

• Mean +/- (2 x standard deviation for particular mean.)
  the number you multiply standard deviation by would be different for the value given in the Q