Statistics

1
Statistics

• Standard Grade Final Revision

2
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.
3
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?
4
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)
5
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) new food
Weight increase ( in Kg) usual food
6
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.
7
The rainfall over a certain period was observed
and the results are given in the diagram above.
Calculate the average rainfall over the period
8
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.
9
Two dice are thrown. Calculate a) p (sum of
the two dice is 9) b) p (sum of two dice is
less than 4)
10
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)
11
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.
12
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.

• A ball is drawn at random from each bag.
• List all the possible outcomes.
• Calculate
• The probability that the sum of the two balls is
  odd.
• b) The probability that the sum of the two balls
  is 6.

13
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.
14
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.
15
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
16
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)