40 Frequency density
30
20
10
Handspan (cm)
0
0
2
4
6
8
10
12
14
16
Median cuts area of histogram in two
Mean is centre of gravity
18
20
22
24
26
28
30
Data: http://www.lifetable.de/
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© MEI 2010
Changing the Mean and Standard Deviation
1.
Which set of statistics belongs with which dot plot?
2.
Can you add one data value to data set 2 to increase the mean and the
standard deviation?
3.
Can you add one data value to data set 1 to reduce the standard deviation
but keep the mean the same?
4.
Can you remove one data value from data set 2 to increase the standard
deviation but keep the mean the same?
5.
Can you remove two data values from data set 1 to increase the standard
deviation but keep the mean the same?
6.
Can you remove one data value from data set 1 to increase the standard
deviation but keep the mean the same?
7.
Challenge question
Can the standard deviation be more than the range? Try to give a convincing
explanation.
© MEI 2010
What does the tree diagram look like?
For each of these, you could get the probability from a tree diagram. You won’t want
to draw the whole tree diagram for some of these but start it off and describe how it
carries on.
Only work out the probabilities once you have got the tree diagrams.
1.
Throw a fair die seven times. What is the probability of getting five 4s?
2.
Throw a fair die five times. What is the probability of three even scores?
3.
Ann and Bill play snooker. For each frame, Ann has a 0.6 chance of winning
and Bill has a 0.4 chance of winning. The winner is the first one to win 3
frames. Find the probability that Bill wins.
4.
Throw a fair die till you get a 6. What is the probability that it takes more than
10 throws?
5.
Choose 6 students at random from a class of 30. The class is half boys and
half girls. What is the probability of choosing 4 girls?
6.
A jury is chosen in an American state which has half the population black.
The jury has 12 members. Assuming jury selection is fair and chooses
members of the population at random, what is the probability of getting an all
white jury?
© MEI 2010