Transcript Statisticsfinal revnppp

Statistics
Standard Grade – Final Revision
The table shows the number of children in a family for a survey carried
out in a large village. Construct a cumulative frequency column
for this table and use it to determine the
median and the semi- interquartile range.
Number of
children
Number of
families
0
38
1
56
2
74
3
31
4
24
5
9
The table shows the favourite holiday destinations
for a group of people. It is intended to use
this information to produce a pie-chart.
What angle in the pie chart will be used to represent
each country chosen?
Country
Italy
U.S.A.
France
Australia
Canada
Germany
Number of
people
13
28
15
9
28
27
The table shows the mode of transport to
school for a number of pupils.
If a pupil is chosen at random calculate
p (Pupil comes to school by bus)
p (Girl who walks)
p (Pupil does not come by car)
Boys
Girls
Car
34
56
Bus
43
40
Walk
55
65
Train
12
8
Tests are to be carried out on a new type of chicken food to see
if the new food significantly increases the weight of the chickens.
Fifteen chickens are given the new food and another fifteen are
fed on the usual chicken food. The weight increases in the
chickens are recorded over a short period of time and these results
are shown in the tables below.
Draw a back to back stem and leaf diagram to compare the figures.
Weight increase ( in Kg) – usual food
Weight increase ( in Kg) – new food
3.6
5.6
4.8
2.2
2.5
1.5
0.9
3.1
3.1
3.4
1.6
3.6
4.3
4.2
3.1
2.8
1.4
2.5
2.9
1.8
3.4
3.3
3.0
4.9
6.3
1.9
1.6
3.3
2.3
3.0
The strength of cables was measured in
an experiment by testing 10 different cables
to breaking point by hanging heavy loads (tons)
at the centre of the cable.
The following results were obtained
∑ loads = 35.9
∑ loads2 = 147.03
Calculate the mean and standard deviation of the
breaking strength of the cables giving
your answers correct to 1 decimal place.
The rainfall over a certain period was observed and the results are
given in the diagram above.
Calculate the average rainfall over the period
A firm employs 32 workers under the age of 18 years
and 45 workers over the age of 18 years.
The average wage of those less
than 18 years is ₤268 per week while the
average age of those over 18 years is ₤282 per week.
Find the average wage for the whole work force.
Two dice are thrown. Calculate
a) p (sum of the two dice is 9)
b) p (sum of two dice is less than 4)
Consider the numbers 2,3,5,8,11,17,20,21,25,30,48,60
One of the numbers is selected at random. Calculate
a) p (multiple of 5)
b) p (factor of 60)
c) p (prime)
The figures below show the total
length, in mm, of starlings captured
during a bird ringing exercise.
184 193 189 214 198 208
Calculate the mean and standard deviation
for these measurements giving your
answers correct to 1 decimal place.
There are two bags A and B.
Bag A contains the numbered balls 1, 2, 3, 4 and 5.
Bag B contains the balls
numbered 3, 4, and 5 as shown in the diagram.
2
1
4
3
Bag A
5
3
4
5
Bag B
A ball is drawn at random from each bag.
List all the possible outcomes.
Calculate
a) The probability that the sum of the two balls is odd.
b) The probability that the sum of the two balls is 6.
The diagram shows pupils marks in Physics and Maths exams.
On the diagram draw what in your opinion is the best fitting
straight line through the points.
Choose two points on this line and find the equation
of the line. Use this equation to estimate the
Maths mark for a pupil who scored 72% in the
Physics exam but missed the Maths exam.
0
00
Marks in Exams
100
90
80
Maths Mark
70
60
50
40
30
20
10
10
20
30
40
50
60
Physics mark
70
80
90
100
A class survey showed the number
of pupils involved in different sports to
be as follows.
Draw an appropriate statistical
diagram to illustrate this information.
Sport
Number
of pupils
Hockey
Football
Rugby
Cricket
7
2
11
3
Athletics
7
A survey was carried out to see how many books
were being carried by pupils in their schoolbags.
The results are shown in the bar chart opposite.
Make up a frequency table and find the mean.
Add in a cumulative frequency column and use
it to determine the median number of
books being carried by pupils
The table shows the number of pupils entering the
Math's competitions held in the school.
If a pupil is selected at random from those entering
the competitions calculate
P (Girl entering a competition)
P (Pupil entering the Intermediate competition)
P (Boy entering the Junior competition)
Boys
Girls
Junior
34
26
Intermediate
28
25
Senior
14
6