Download NIS Probability and Statistics Diagnostic

NIS Probability and Statistics Diagnostic Test
Predict a "likely" or "unlikely" event
Q1
Which is the most likely event;
a. Snowing in Melbourne in summer
b. Rolling a 4 using a dice
c. Tossing a head using a coin
Construct a bar graph when given data
Q2
In my class 5 people have blue eyes, 14 people have brown eyes, 2 people
have green eyes and 3 people have hazel coloured eyes.
Draw a bar graph to show this information.
Correctly use common fraction names
Q3
Write the fraction for the following
a)
one third
b)
seven eighths
c)
a quarter
Use a number line between 0 and 1 to place common fractions
Q4
Mark the fractions on the number line as accurately as you can
0
1
Describe an outcome as "certain", "likely", "unlikely" or "never"
Q5
Give one example of each of the following words
Certain
Likely
Unlikely
Never
Identify equivalent fractions
Q6
Which (one or more) of the following fractions is equivalent to two thirds?
Circle correct fraction(s)
5
6
1
2
4
6
6
8
6
9
Arrange given simple data into a frequency table
Answer questions about the likelihood of an event
Q7
A
The class was surveyed about how many pets they had and this data was
collected
2, 2, 2, 3, 4, 5, 2, 7, 5, 0, 4, 6, 3, 2, 0, 0, 1, 1,2, 0
Complete a frequency table for this data
Number Tally
B
Frequency
If you picked a person at random from the class what is the most likely
number of pets they would have?
Write common fractions with a denominator of 100
Recognise how fractions with a denominator of 100 can be written as a percentage
Q8
Write these fractions as percentages
1
=
4
1
=
10
3
=
4
1
=
5
Display the sample space of a single step experiment
Q9
A day is to be chosen from a week.
List the total sample space.
Recognises a set of data as discrete
Recognises a set of data as continuous
Q10 Write the letter C if the following data is continuous
Write the letter D if the data is discrete
a)
b)
c)
Shoe sizes of people in my class
Distance each person lives from school
Number of sisters each person has
Associate the link between the number range 0-1 with the language of certain, highly
likely, likely, unlikely, highly unlikely and never
Q11
Assign a probability as a percentage
Assign a probability as a fraction
Assign a probability as a decimal
Assign a probability in percentage, decimal or fraction format
Q12 For the spinner shown below
a)
What is P(4) as a fraction?
b)
What is P(3) as a decimal?
c)
What is P(5) as a percentage?
Equivalence between common fractions, decimal and percentages, e.g. 1/2, 0.5 and
50% between 0 and 1
1
Q13 Write these numbers in order of highest to lowest , 20%, 0.6, 0.58
4
Calculates different measures of central location - mean, median and mode
Calculate the range of a set of data
Q14
A
For the data;
2, 3, 4, 2, 5, 2, 1, 1
a) Calculate the mean
b) Determine the median
c) Determine the mode
d) Find the range
Interpret mean, median and mode
B
If I add the number 10 to the data above, circle what happens to each
a)
b)
c)
d)
Mean
Median
Mode
Range
increases
increases
increases
increases
stays the same
stays the same
stays the same
stays the same
decreases
decreases
decreases
decreases
Distinguishes between discrete and continuous data
Q15 Circle the type of data each of these is.
a) Shoes size
Discrete
Continuous
b) Height
Discrete
Continuous
c) Number of brothers Discrete
Continuous
Read information off a graph, e.g. bar graph (Discrete data)
Draw a simple bar graph given a set of categorical data
Q16
Colour
Blue
Red
Green
Black
Purple
Frequency
3
5
3
1
7
Draw a histogram that displays the data in the table above
List the sample space of a two-step experiment, e.g. rolling two dice
Q17
List the sample space showing all possible outcomes of tossing a coin and
rolling a dice
Calculates the probability of an outcome, given the sample space, e.g. tree diagram
Q18 Calculate the probability of tossing three heads in a row
Calculates the probability of an event with replacement
Q19 A bag contains 20 red and 20 blue balls. What is the probability of selecting
two blue balls taken out at the same time?
Interpret a Stem and leaf plot (Continuous data)
Q20
The Stem and Leaf Plot below is of the ages of people in a doctor’s waiting
room.
02338
1024
236
3 1
15 = 15
a)
What fraction of the people are younger than 10?
b)
Which age is the most frequent?
c)
What is the median age?
Interpret a Histogram (Continuous data)
Q21
a) How many people have heights between 159.5 and 169.5 cm?
b) In which interval does the mean probably lie?
Given a probability, predict how many times an event might occur
Q22 How many 5s would you expect to roll if you rolled a dice 600 times?
Calculate conditional probability
Q23 I travel to work by route A or route B. The probability that I chose route A is
1
2
. The probability that I am late for work if I go via route A is
and if I go
4
3
1
via route B the probability that I am late is
3
(a) What is the probability that I am late for work on Monday?
(b) Given that I am late for work, what is the probability that I went via route B?
Create intervals from ungrouped data
Q24 The marks obtained by 40 students in a recent exam are given below:
16, 17, 18, 3, 7, 23, 18, 13, 10, 21, 7, 1, 13, 21, 13, 15, 19, 24,
16, 2, 23, 5, 12, 18, 8, 12, 6, 8, 16, 5, 3, 5, 0, 7, 9, 12, 20, 10, 2, 23
Divide the data into five groups and present the data in a frequency table.
Interprets a Box and Whisker Plot representing continuous data
Q25
a) What is the range for this box-and-whisker plot?
b) What is the median for the above diagram?
c) What percentage of weeks where more than 40 TVs sold?