GCSE Statistics Specimen Paper

1
GCSE Statistics Specimen Paper

• Revision Notes

2
GCSE Statistics Specimen (H)

• Section A

3
Need single digits in the range 1, , 6 so
ignore 0 and gt6. Treat sequence as 28 single
digit numbers.
4
Misleading because a) Tilt distorts areas b)
Slice pulled out
5
Population is all those who can be included in
the (stratified) sample. Check validity of data -
honesty, up-to-date etc.
6
Composite means made up of two or more
components. One bar for each cereal, either or
per serving. SW best choice.
7
It is a RANK scale. 174 youths aged 18-24 yrs old
were sampled. 19 of these said Very well. This
percentage declines with age.
8
The task is to identify which of maps B, C and D
most closely echoes the distribution in map A.
Rainfall is partly similar, but altitude is a
better match.
9
The probabilities on any set of branches must
always total 1. (Why?) Reaching the top could be
either Dry AND Top (Multiply) OR (Add) Wet AND
Top (Multiply). Given the top is reached, P(Wet)
Proportion of successful climbs which came from
wet conditions.
10
A BIASED sample is one which is not
representative of the whole population being
studied. A Pilot survey is a dry run to iron
out any problems. Simple Random sampling is not
Systematic but simply random, e.g. names out of a
hat or Ran.
11
Comparative box plots MUST be drawn on the same
horizontal scale, one above the other. Weight
alone will never make you certain about the sex
of the tortoise, but you can be persuaded beyond
reasonable doubt. Use the UQ and LQ (lt520 F and
gt1220 M) to illustrate your answer in detail.
12
GCSE Statistics Specimen (H)

• Section B

13
Dont mess up on these easy marks! Line up the
Leaves and arrange them in order. Median at
position (N1)/2 8. LQ at position (71)/2 from
the Min. UQ at position (71)/2 from the Max. IQR
UQ - LQ
14
You MUST learn the Outlier formula. If m lt LQ -
1.5 x IQR or m gt UQ 1.5 x IQR then m is an
outlier. The mean is changed more than the
median because only the former is affected by
outliers.
15
Its always worth spending time on a page even
when there is no question. Make sure you
understand the data and context. Here we have two
seasons data presented - one as a bar chart and
one as a table. Hmm - looks like we might be
asked to compare them
16
Since this is Higher Tier, you should be able to
manage the calculations! 9 12 39 60 goals
for 2002/36 21 21 42 goals for 2001/2
represented by 6cm diameter. 2002/3 Diameter For
2 marks you should make 2 comments in Part (b).
17
You know this will be 4-point moving averages
because the data are given by quarter. To make it
easier for you, they actually tell you it is
going to be 4-point moving averages. To make it
even easier still, they tell you how to work them
out. Not much left to think about, really.
18
The trend line is a line of best fit through the
moving averages. Use triangles to find its
y-intercept (c) and its gradient (m) and then the
equation of the trend line is y mx c
19
The mean seasonal effect given is the distance
between the trend line and the actual value.
Since it is positive for the first quarter, we
know that the trend line is ABOVE the first
quarter profits. Use the trend line to predict
the y value when the x value is (2004 first
quarter), then SUBTRACT the 0.05 figure
quoted. Write your answer (which is in millions
of pounds) as an ordinary number.
20
Always use any examples given to guide you if the
context looks a little unfamiliar. Look carefully
at that top row!
Remember that for Histograms Frequency
Interval Width x Frequency Density Use the
Sigma fx formula for the mean estimate.
21
Use your table to complete the histogram.
The bump is on the right and the tail is pulled
to the left so it is a NEGATIVELY skewed
distribution.
22
Standardised scores enable you to compare
statistics from two different distributions.
A positive SS is above average, while a negative
SS is below average. 65 of results are between
1. 95 of results are between 2 and 99.8 of
results are between 3. Learn these!!
23
You can guarantee you will get a visit from Mr
Spearman. Note that Territory is already ranked.
Note that it is LARGEST to SMALLEST! Do the same
for Wing Length. Now do the old d and d2
routine. A value within 0.5 is weak or
non-existent correlation. It becomes stronger the
closer it gets to 1. If it goes beyond 1 then
do it again! You messed up!
24
Dont be put off by the language. Take it
literally. 36 have a video player - some of these
may have a DVD player too, 16 in fact. Thus 20
have a video only. Similarly, 50 - 16 34 houses
with just a DVD player. The Venn diagram contains
20 and 34 in the circles and 16 in the overlap,
with the remaining 50 outside. Neither means Not
A AND (x) Not B.
25
95 means 2 s.d. 99.8 means 3 s.d. Warning
38 0.52 Action 38 0.72 We also check the
Variance to make sure the s.d. is not
changing. WARNING means take another sample
immediately. ACTION means stop and reset the
machine.