Mean and Standard Deviation
1. Adam and Barry play for the Ketterby cricket team.
Here are their scores in their last 10 innings:
Adam
13
126
64
37
63
27
0
102
12
56
Barry
61
54
40
47
62
32
39
69
43
53
Which would you pick for an important game?
2. Super Crisps come in 25g bags. There are two machines producing the crisps. A quality
control engineer weighs a sample of 10 bags from each machine.
Machine A
25.3
25.6
24.8
25.7
25.5
25
24.9
25.7
25.5
25.6
Machine B
25.3
25.3
25.4
24.9
25.3
25.3
25.4
25.4
25.4
25.3
Work out the mean and standard deviation for each machine.
Super Crisps will be taken to court if it is found their bags are less than 25g. Which
machine gives the best chance of avoiding this fate?
3. ZupaPharm have developed a drug that is supposed to cause weight gain. It is tested on
a sample of 50 rats. The results gave a mean weight gain of 12g with a standard deviation
of 30g.
Work out a 95% confidence interval for the mean weight gain. Can you be “95% sure” that
the drug actually causes weight gain in rats?
4. Samples of fish are taken and weighed from two lakes.
Lake P: 10 fish, mean 156g, s.d. 38g
Lake Q: 20 fish, mean 240g, s.d. 121g
Work out 90% confidence intervals for each lake. Is there evidence (at the 90% level) of a
real difference in the weights of fish in the two lakes?
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2004-04-19
Mean and Standard Deviation
• The mean is the average value. Add them up then divide by how many there are.
• The standard deviation is a measure of how spread out (or varied) the data is.
• A large standard deviation suggests there is a lot of variation.
• Common symbols for the mean are µ (mu), x (x-bar) and m.
• Common symbols for the standard deviation are σ (sigma) and s.
For other than very simple examples the only sensible way to calculate the standard
deviation is to use the statistics functions on a calculator, or use a computer.
On a calculator:
• Enter statistics mode on the calculator.
• Clear the statistics memory (typically [Scl])
• Enter the data. Type each number