In the two weeks leading up to a half marathon, Rogan ran the following distances, in kilometres.
`15, \ 21, \ 17, \ 9, \ 17, \ 25, \ 11`
What was his mean distance, in kilometres? Give your answer correct to 2 decimal places? (2 marks)
Aussie Maths & Science Teachers: Save your time with SmarterEd
In the two weeks leading up to a half marathon, Rogan ran the following distances, in kilometres.
`15, \ 21, \ 17, \ 9, \ 17, \ 25, \ 11`
What was his mean distance, in kilometres? Give your answer correct to 2 decimal places? (2 marks)
`16.43` km
`text(Mean)` | `= (15 + 21 + 17 + 9 + 17 + 25 + 11)/7` |
`= (115)/7` | |
`= 16.4285…` | |
`~~ 16.43` km |
The points scored by an AFL team in their first 13 games of the season is recorded.
`78, \ 84, \ 63, \ 75, \ 98, \ 105, \ 92, \ 75, \ 84, \ 96, \ 84, \102, \100`
In the 14th game, they scored 61.
Which of these values would increase?
`B`
`text(Consider each option:)`
`text(Mode – unchanged at 84)`
`text(Range – increases from 42 to 44)`
`text(Mean – decreases from 87.38 to 85.5)`
`text{Median – unchanged at 84}`
`=>B`
Jacqui's basketball team has 5 players.
The height of each player is listed below (in cm):
`186, 190, 164, 190, 175`
What is the median height of these players?
`C`
`text(Heights in order are:)`
`164, 175, 186, 190, 190`
`:.\ text(Median) = 186\ text(cm)`
`=> C`
This table shows the number of people who visited a war memorial on weekdays over 4 weeks.
--- 1 WORK AREA LINES (style=lined) ---
--- 1 WORK AREA LINES (style=lined) ---
--- 1 WORK AREA LINES (style=lined) ---
--- 1 WORK AREA LINES (style=lined) ---
a. `44`
b. `26`
c. `39`
d. `22`
a. `text(Range on Mondays)` | `= 81 \ -\ 37` |
`= 44` |
b. `text(Mean on Fridays)` | `=(22 + 32+28+22)/4` |
`=104/4` | |
`=26` |
c. `text(Week 3 data in order: 28, 37, 39, 53, 72)`
`text(Median Week 3)` | `=\ text(middle score)` |
`=\ 39` |
d. `text(Modal number of visitors) = 22`
The mean (average) of four numbers is 26.
One more number is added and the mean number becomes 27.
What is the number that was added? (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
`31`
`text(Total of the first 4 numbers,)`
`26 xx 4 = 104`
`text(Total including the 5th number added,)`
`27 xx 5 = 135`
`:.\ text(The number added)` | `=135-104` |
`=31` |
Percy bought 8 packets of cough lollies for $18.00.
The average cost of one packet is
`B`
`text(Price of 1 packet)` | `= ($18.00)/8` |
`= $2.25` |
`=>B`
Each number from 1 to 30 is written on a separate card. The 30 cards are shuffled. A game is played where one of these cards is selected at random. Each card is equally likely to be selected.
Ezra is playing the game, and wins if the card selected shows an odd number between 20 and 30.
--- 1 WORK AREA LINES (style=lined) ---
--- 4 WORK AREA LINES (style=lined) ---
a. `21, 23, 25, 27, 29`
b. | `Ptext{(not win)}` | `=1-Ptext{(win)}` |
`=1-5/30` | ||
`=25/30` | ||
`=5/6` |
In a bag, there are six playing cards, 2, 4, 6, 8, Queen and King. The Queen and King are known as picture cards.
Two of these cards are chosen randomly. All the possible outcomes are shown.
--- 2 WORK AREA LINES (style=lined) ---
--- 2 WORK AREA LINES (style=lined) ---
a. `P text{(at least 1 picture card)} = 9/15`
b. | `P text{(no picture card)}` | `= 1 – 9/15` |
`= 6/15` |
A survey of which of the following would provide data that are both categorical and
nominal?
`A`
`text(By elimination:)`
`text{Qualitative (not quantitative)}`
`text{→ Eliminate B and C}`
`text(Nominal data is not ordered)`
`text{→ Eliminate D}`
`=> A`
Barbara plays a game of chance, in which two unbiased six-sided dice are rolled. The score for the game is obtained by finding the difference between the two numbers rolled. For example, if Barbara rolls a 2 and a 5, the score is 3.
The table shows some of the scores.
--- 3 WORK AREA LINES (style=lined) ---
a.
b. | `Ptext{(not zero)}` | `= frac{text(numbers) ≠ 0}{text(total numbers)}` |
`= frac{30}{36}` | ||
`= frac{5}{6}` |
\(\text{Alternate solution (b)}\)
b. | `Ptext{(not zero)}` | `= 1 – Ptext{(zero)}` |
`= 1 – frac{6}{36}` | ||
`= frac{5}{6}` |
Which histogram best represents a dataset that is positively skewed?
`A`
`text(Positive skew occurs when the tail on the)`
`text{histogram is longer on the right-hand}`
`text{(positive) side.}`
`=> \ A`
The faces on a biased six-sided die are labelled 1, 2, 3, 4, 5 and 6. The die was rolled twenty times. The relative frequency of rolling a 6 was 30% and the relative frequency of rolling a 2 was 15%. The number 3 was the only other number rolled in the twenty rolls.
How many times was the number 3 rolled in the twenty rolls of the die? (3 marks)
--- 4 WORK AREA LINES (style=lined) ---
`11`
`text(Number of 6’s) = 30/100 xx 20 = 6`
`text(Number of 2’s) = 15/100 xx 20 = 3`
`:.\ text(Number of 3’s)` | `= 20 – (6 + 3)` |
`= 11` |
A roulette wheel has the numbers 0, 1, 2, …, 36 where each of the 37 numbers is equally likely to be spun.
If the wheel is spun 18 500 times, calculate the expected frequency of spinning the number 8. (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
`500`
`P(8) = 1/37`
`:.\ text(Expected Frequency (8))`
`= 1/37 xx 18\ 500`
`= 500`
A survey asked the following question for students born in Australia:
"Which State or Territory were you born in?"
How would the responses be classified?
`B`
`text{The data is categorical (not numerical) since}`
`text(the name of a State is required.)`
`text(This data cannot be ordered.)`
`=> B`
Jeremy rolled a biased 6-sided die a number of times. He recorded the results in a table.
\begin{array} {|l|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \text{Number} \rule[-1ex]{0pt}{0pt} & \ \ 1 \ \ & \ \ 2 \ \ & \ \ 3 \ \ & \ \ 4 \ \ & \ \ 5 \ \ & \ \ 6 \ \ \\
\hline
\rule{0pt}{2.5ex} \text{Frequency} \rule[-1ex]{0pt}{0pt} & \ \ 23 \ \ & \ \ 19 \ \ & \ \ 48 \ \ & \ \ 20 \ \ & \ \ 21 \ \ & \ \ 19 \ \ \\
\hline
\end{array}
What is the relative frequency of rolling a 3? (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
\(\dfrac{8}{25}\)
\(\text{Rel Freq}\) | \(=\dfrac{\text{number of 3’s rolled}}{\text{total rolls}}\) |
\(=\dfrac{48}{150}\) | |
\(=\dfrac{8}{25}\) |
During a year, the maximum temperature each day was recorded. The results are shown in the table.
From the days with a maximum temperature less than 25°C, one day is selected at random.
What is the probability, to the nearest percentage, that the selected day occurred during winter?
`text(C)`
`text{P(winter day)}` | `= (text(winter days < 25))/text(total days < 25) xx 100` |
`= 71/223 xx 100` | |
`= 31.8…%` |
`=>\ text(C)`
A set of data is summarised in this frequency distribution table.
Which of the following is true about the data?
`text(B)`
`text{Mode = 7 (highest frequency of 9)}`
`text(Median = average of 15th and 16th data points.)`
`:.\ text(Median = 6)`
`=>\ text(B)`
An experiment has three distinct outcomes, A, B and C.
Outcome A occurs 50% of the time. Outcome B occurs 23% of the time.
What is the expected number of times outcome C would occur if the experiment is conducted 500 times?
`text(B)`
`text(Expectation of outcome)\ C`
`= 1 – 0.5 – 0.23`
`= 0.27`
`:.\ text(Expected times)\ C\ text(occurs)`
`= 0.27 xx 500`
`= 135`
`=>\ text(B)`
A survey asked the following question.
'How many brothers do you have?'
How would the responses be classified?
`text(C)`
`text(The number of brothers a person has is)`
`text(an exact whole number.)`
`:.\ text(Classification is numerical, discrete.)`
`=>\ text(C)`
The faces on a twenty-sided die are labelled $0.05, $0.10, $0.15, … , $1.00.
The die is rolled once.
What is the probability that the amount showing on the upper face is more than 50 cents but less than 80 cents?
A. `1/4`
B. `3/10`
C. `7/20`
D. `1/2`
`A`
`text(Possible faces that satisfy are:)`
`55text(c),60text(c),65text(c),70text(c),75text(c)`
`:.\ text(Probability)` | `= 5/20` |
`= 1/4` |
`=>A`
In a survey of 200 randomly selected Year 12 students it was found that 180 use social media.
Based on this survey, approximately how many of 75 000 Year 12 students would be expected to use social media?
A. 60 000
B. 67 500
C. 74 980
D. 75 000
`B`
`text(Expected number)` | `= 180/200 xx 75\ 000` |
`= 67\ 500` |
`=> B`
Which set of data is classified as categorical and nominal?
`A`
`text(Categorical and nominal data is)`
`text(qualitative and not ordered.)`
`=> A`
The table shows the relative frequency of selecting each of the different coloured jelly beans from packets containing green, yellow, black, red and white jelly beans.
\begin{array} {|c|c|}
\hline
\rule{0pt}{2.5ex} \textit{Colour} \rule[-1ex]{0pt}{0pt} & \textit{Relative frequency} \\
\hline
\rule{0pt}{2.5ex} \text{Green} \rule[-1ex]{0pt}{0pt} & 0.32 \\
\hline
\rule{0pt}{2.5ex} \text{Yellow} \rule[-1ex]{0pt}{0pt} & 0.13 \\
\hline
\rule{0pt}{2.5ex} \text{Black} \rule[-1ex]{0pt}{0pt} & 0.14 \\
\hline
\rule{0pt}{2.5ex} \text{Red} \rule[-1ex]{0pt}{0pt} & \\
\hline
\rule{0pt}{2.5ex} \text{White} \rule[-1ex]{0pt}{0pt} & 0.24 \\
\hline
\end{array}
--- 2 WORK AREA LINES (style=lined) ---
--- 2 WORK AREA LINES (style=lined) ---
i. \(\text{Relative frequency of red}\)
\(= 1-(0.32 + 0.13 + 0.14 + 0.24)\)
\(= 1-0.83\)
\(= 0.17\)
ii. \(P\text{(not selecting black)}\)
\(= 1-P\text{(selecting black)}\)
\(= 1-0.14\)
\(= 0.86\)
On a school report, a student’s record of completing homework is graded using the following codes.
C = consistently
U = usually
S = sometimes
R = rarely
N = never
What type of data is this?
`A`
`text(The data has been grouped into categories and)`
`text(because each category can be ranked, it is ordinal.)`
`⇒ A`
`text(Reasons the graph is misleading include)`
`text(- the columns are a different widths/volumes)`
`text(- the vertical axis doesn’t start at zero)`
`text(Reasons the graph is misleading include)`
`text(- the columns are a different widths/volumes)`
`text(- the vertical axis doesn’t start at zero)`
The sector graph shows the proportion of people, as a percentage, living in each region of Sumcity. There are 24 000 people living in the Eastern Suburbs.
--- 1 WORK AREA LINES (style=lined) ---
Jake used the information above to draw a column graph.
Identify this region and justify your answer. (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
i. `text(Let the population of Sumcity =)\ P`
`text(15%)× P` | `= 24\ 000` |
`:.P` | `= (24\ 000)/0.15` |
`= 160\ 000\ …\ text(as required)` |
ii. `text(Western Suburbs population)`
`= text(10%) × 160\ 000`
`= 16\ 000`
`text(The column graph has this population as)`
`text(12 000 people which is incorrect.)`
`21\ \ \ 45\ \ \ 29\ \ \ 27\ \ \ 19\ \ \ 35\ \ \ 23\ \ \ 58\ \ \ 34\ \ \ 27` (2 marks)
--- 6 WORK AREA LINES (style=blank) ---
--- 2 WORK AREA LINES (style=lined) ---
--- 2 WORK AREA LINES (style=lined) ---
The diagram shows a spinner.
The arrow is spun and will stop in one of the six sections.
What is the probability that the arrow will stop in a section containing a number greater
than 4?
`D`
`P\ text((number greater than 4))`
`= P(7) + P (9)`
`= 2/6 + 1/6`
`= 1/2`
`=> D`
The mean of a set of 5 scores is 62.
What is the new mean of the set of scores after a score of 14 is added?
`B`
`text(Mean of 5 scores) = 62`
`:.\ text(Total of 5 scores) = 62 xx 5 = 310`
`text(Add a score of 14)`
`text(Total of 6 scores) = 310 + 14 = 324`
`:.\ text(New mean)` | `= 324/6` |
`= 54` |
`=> B`
Kay randomly selected a marble from a bag of marbles, recorded its colour and returned it to the bag. She repeated this process a number of times.
Based on these results, what is the best estimate of the probability that Kay will choose a green marble on her next selection?
`C`
`text{P(Green)}` | `= text(# Green chosen) / text(Total Selections)` |
`= 4/24` | |
`= 1/6` |
`=> C`
Marcella is planning to roll a standard six-sided die 60 times.
How many times would she expect to roll the number 4?
`B`
`P(4) = 1/6`
`:.\ text(Expected times to roll 4)`
`= 1/6 xx text(number of rolls)`
`= 1/6 xx 60`
`= 10`
`=> B`
The probability of an event occurring is `9/10.`
Which statement best describes the probability of this event occurring?
`A`
`text(The event is highly likely to occur)`
`text(but not certain.)`
`=> A`
Four radio stations reported the probability of rain as shown in the table.
Which radio station reported the highest probability of rain?
`D`
`text(Converting all probabilities to decimals)`
`2AT` | `= 0.53` |
`2BW` | `= 0.17` |
`2CZ` | `= 0.52` |
`2DL` | `= 0.60` |
`=> D`
What is the mean of the set of scores?
`3, \ 4, \ 5, \ 6, \ 6, \ 8, \ 8, \ 8, \ 15`
`B`
`text(Mean)` | `= ((3 + 4 + 5 +6 + 6 + 8 + 8 + 8 + 15))/9` |
`= 63/9` | |
`= 7` |
`=> B`
This sector graph shows the distribution of 116 prizes won by three schools: X, Y and Z.
How many prizes were won by School X?
`B`
`text(Centre angle of School X sector)`
`= 100^@\ text{(by measurement)}`
`:.\ text(Prizes won by school X)`
`= 100/360 xx 116`
`= 32.22\ …`
`=> B`
Use the set of scores 1, 3, 3, 3, 4, 5, 7, 7, 12 to answer Questions 6 and 7.
Question 6
What is the range of the set of scores?
Question 7
What are the median and the mode of the set of scores?
`text(Question 6:)\ C`
`text(Question 7:)\ D`
`text(Question 6)`
`text(Range)` | `= text(High) – text(Low)` |
`= 12 – 1` | |
`= 11` |
`=> C`
`text(Question 7)`
`text(9 scores)`
`:.\ text(Median)` | `= (9 + 1) / 2` |
`=5 text(th score)` | |
`= 4` |
`text(Mode) = 3`
`=> D`
Which fraction is equal to a probability of `text(25%)`?
`B`
`P=25/100=1/4`
`=> B`
Give an example of an event that has a probability of exactly `3/4`. (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
`text(Choosing a red ball out of a bag that)`
`text(contains 3 red balls and 1 green ball.)`
`text {(} text(An infinite amount of examples are)`
`text(possible) text{).}`
`text(Choosing a red ball out of a bag that contains)`
`text(3 red balls and 1 green ball.)`
`text {(} text(An infinite amount of examples are)`
`text(possible) text{).}`
Consider the following set of scores:
`3, \ 5, \ 5, \ 6, \ 8, \ 8, \ 9, \ 10, \ 10, \ 50.`
--- 1 WORK AREA LINES (style=lined) ---
--- 5 WORK AREA LINES (style=lined) ---
`text(would become lower.)`
`text(Median will NOT change.)`
i. `text(Total of scores)`
`= 3 + 5 + 5 + 6 + 8 + 8 + 9 + 10 + 10 +50`
`= 114`
`:.\ text(Mean) = 114/10 = 11.4`
ii. `text(Mean)`
`text{If the outlier (50) is removed, the mean}`
`text(would become lower.)`
`text(Median)`
`text(The current median (10 data points))`
`= text(5th + 6th)/2 = (8 + 8)/2 = 8`
`text(The new median (9 data points))`
`=\ text(5th value)`
`= 8`
`:.\ text(Median will NOT change.)`
Each student in a class is given a packet of lollies. The teacher records the number of red lollies in each packet using a frequency table.
What is the relative frequency of a packet of lollies containing more than three red lollies?
`A`
`text(# Packets with more than 3)`
`= 3 + 1 = 4`
`text(Total packets) = 19`
`:.\ text(Relative Frequency) = 4/19`
`=> A`
The graph shows the predicted population age distribution in Australia in 2008.
--- 1 WORK AREA LINES (style=lined) ---
--- 1 WORK AREA LINES (style=lined) ---
--- 4 WORK AREA LINES (style=lined) ---
--- 2 WORK AREA LINES (style=lined) ---
`text(and is not restricted by a 5-year limit.)`
i. | `text{# Females (0-4)}` | `= 0.6 xx 1\ 000\ 000` |
`= 600\ 000` |
ii. | `text(Modal age group)\ =` | `text(35 – 39)` |
iii. | `text{# Males (15-19)}` | `= 0.75 xx 1\ 000\ 000` |
`= 750\ 000` |
`text{# Females (15-19)}` | `= 0.7 xx 1\ 000\ 000` |
`= 700\ 000` |
`:.\ text{Total People (15-19)}` | `= 750\ 000 + 700\ 000` |
`= 1\ 450\ 000` |
iv. | `text(The 80+ group includes all people over 80)` |
`text(and is not restricted by a 5-year limit.)` |
Christina has completed three Mathematics tests. Her mean mark is 72%.
What mark (out of 100) does she have to get in her next test to increase her mean mark to 73%? (2 marks)
--- 5 WORK AREA LINES (style=lined) ---
`76`
`text(Total marks in 3 tests)`
`= 3 xx 72`
`= 216`
`text(We need 4-test mean) = 73`
`text(i.e.)\ \ \ ` | `text{Total Marks (4 tests)}-:4` | `= 73` |
`text(Total Marks)\ text{(4 tests)}` | `= 292` |
`:.\ text(4th test score)` | `= 292 – 216` |
`= 76` |
In a survey, 450 people were asked about their favourite takeaway food. The results are displayed in the bar graph.
How many people chose pizza as their favourite takeaway food? (2 marks)
`175`
`text(Number of people who chose pizza)`
`= text{Length of pizza section}/text{Total length of bar} xx 450`
`~~ 7/18 xx 450`
`~~ 175`
`:.\ 175\ text(people chose pizza.)`
A bag contains some marbles. The probability of selecting a blue marble at random from this bag is `3/8`.
Which of the following could describe the marbles that are in the bag?
`D`
`P(B) = 3/8`
`text(In)\ A,\ \ ` | `P(B) = 3/11` |
`text(In)\ B,\ \ ` | `P(B) = 6/17 ` |
`text(In)\ C,\ \ ` | `P(B) = 3/11` |
`text(In)\ D,\ \ ` | `P(B) = 6/16 = 3/8` |
`=> D`
The height of each student in a class was measured and it was found that the mean height was 160 cm.
Two students were absent. When their heights were included in the data for the class, the mean height did not change.
Which of the following heights are possible for the two absent students?
`C`
`text(S) text(ince the mean doesn’t change)`
`=>\ text(2 absent students must have a)`
`text(mean height of 160 cm.)`
`text(Considering each option given,)`
`(149 + 171) -: 2 = 160`
`=> C`
The stem-and-leaf plot represents the daily sales of soft drink from a vending machine.
If the range of sales is 43, what is the value of | ? |
`A`
`text(Range = High) – text(Low) = 43`
`:.\ 67 – text(Low)` | `= 43` |
`text(Low)` | `= 24` |
`:.\ N = 4`
`=> A`
The graph below displays data collected at a school on the number of students
in each Year group, who own a mobile phone.
--- 1 WORK AREA LINES (style=lined) ---
Which student is more likely to own a mobile phone?
Justify your answer with suitable calculations. (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
--- 2 WORK AREA LINES (style=lined) ---
i. `text(Year 12 (100%))`
ii. | `text(% Ownership in Year 9)` | `=55/70` |
`=\ text{78.6% (1d.p.)}` | ||
`text(% Ownership in Year 10)` | `=50/60` | |
`=\ text{83.3% (1d.p.)}` |
`:.\ text(The Year 10 student is more likely to own a mobile phone.)`
iii. `text(% Ownership increases as students)`
`text(progress from Year 7 to Year 12.)`
A die was rolled 72 times. The results for this experiment are shown in the table.
\begin{array} {|c|c|}
\hline
\rule{0pt}{2.5ex} \textit{Number obtained} \rule[-1ex]{0pt}{0pt} & \textit{Frequency} \\
\hline
\rule{0pt}{2.5ex} \ 1 \rule[-1ex]{0pt}{0pt} & 16 \\
\hline
\rule{0pt}{2.5ex} \ 2 \rule[-1ex]{0pt}{0pt} & 11 \\
\hline
\rule{0pt}{2.5ex} \ 3 \rule[-1ex]{0pt}{0pt} & \textbf{A} \\
\hline
\rule{0pt}{2.5ex} \ 4 \rule[-1ex]{0pt}{0pt} & 8 \\
\hline
\rule{0pt}{2.5ex} \ 5 \rule[-1ex]{0pt}{0pt} & 12 \\
\hline
\rule{0pt}{2.5ex} \ 6 \rule[-1ex]{0pt}{0pt} & 15 \\
\hline
\end{array}
--- 1 WORK AREA LINES (style=lined) ---
--- 1 WORK AREA LINES (style=lined) ---
--- 1 WORK AREA LINES (style=lined) ---
i. \(\text{Since die rolled 72 times}\) |
\(\therefore\ A\) | \(=72-(16+11+8+12+15)\) |
\(=72-62\) | |
\(=10\) |
ii. \(\text{Relative frequency of 4}\) | \(=\dfrac{8}{72}\) |
\(=\dfrac{1}{9}\) |
iii. \(\text{Expected frequency of any number}\) |
\(=\dfrac{1}{6}\times 72\) |
\(=12\) |
\(\therefore\ \text{5 was obtained the expected number of times.}\) |
The heights of the players in a basketball team were recorded as 1.8 m, 1.83 m, 1.84 m, 1.86 m and 1.92 m. When a sixth player joined the team, the average height of the players increased by 1 centimetre.
What was the height of the sixth player?
`C`
`text(Old Mean)` | `=(1.8+1.83+1.84+1.86+1.92)-:5` |
`=9.25/5` | |
`=1.85\ \ text(m)` |
`text{S}text{ince the new mean = 1.86m (given)}`
`text(New Mean)` | `=text(Height of all 6 players) -: 6` |
`:.1.86` | `=(9.25+h)/6\ \ \ \ (h\ text{= height of new player})` |
`h` | `=(6xx1.86)-9.25` |
`=1.91\ \ text(m)` |
`=> C`
A data set of nine scores has a median of 7.
The scores 6, 6, 12 and 17 are added to this data set.
What is the median of the data set now?
`B`
`text(S)text(ince an even amount of scores are added below and)`
`text(above the existing median, it will not change.)`
`=>B`
Jason travels to work by car on all five days of his working week, leaving home at 7 am each day. He compares his travel times using roads without tolls and roads with tolls over a period of 12 working weeks.
He records his travel times (in minutes) in a back-to-back stem-and-leaf plot.
--- 1 WORK AREA LINES (style=lined) ---
--- 1 WORK AREA LINES (style=lined) ---
--- 5 WORK AREA LINES (style=lined) ---
`text(Skewness)`
i. `text(Modal time) = 52\ text(minutes)`
ii. `text(30 times with no tolls)`
`text(Median)` | `=\ text(Average of 15th and 16th)` |
`=(50 + 51)/2` | |
`= 50.5\ text(minutes)` |
iii. `text(Spread)`
`text{Times without tolls have a much tighter}`
`text{spread (range = 22) than times with tolls}`
`text{(range = 55).}`
`text(Skewness)`
`text(Times without tolls shows virtually no skewness)`
`text(while times with tolls are positively skewed.)`
Write down a set of six data values that has a range of 12, a mode of 12 and a minimum value of 12. (2 marks)
`12, 12, 12, 16, 18, 24`
`12, 12, 12, 16, 18, 24`
`text(NB. There are many correct solutions.)`
On Saturday, Jonty recorded the colour of T-shirts worn by the people at his gym. The results are shown in the graph.
--- 1 WORK AREA LINES (style=lined) ---
--- 2 WORK AREA LINES (style=lined) ---
i. `text(# People)` | `=5+15+10+3+1` |
`=34` |
ii. `P (B\ text{or}\ G)` | `=P(B)+P(G)` |
`=5/34+10/34` | |
`=15/34` |
This back-to-back stem-and-leaf plot displays the test results for a class of 26 students.
What is the median test result for the class?
`B`
`text(26 results given in the data)`
`=>text(Median is average of)\ 13^text(th)\ text(and)\ 14^text(th)`
`:.\ text(Median)` | `=(45+47)/2` |
`=46` |
`=>B`
The diagram below shows a stem-and-leaf plot for 22 scores.
--- 1 WORK AREA LINES (style=lined) ---
--- 1 WORK AREA LINES (style=lined) ---
i. `text(Mode) = 78`
ii. `22\ text(scores)`
`=>\ text(Median is the average of 11th and 12th scores)`
`:.\ text(Median)` | `= (45 + 47)/2` |
`= 46` |
A wheel has the numbers 1 to 20 on it, as shown in the diagram. Each time the wheel is spun, it stops with the marker on one of the numbers.
The wheel is spun 120 times.
How many times would you expect a number less than 6 to be obtained?
`C`
`P(text(number < 6) ) = 5/20 = 1/4`
`:.\ text(Expected times)` | `= 1/4 xx text(times spun)` |
`= 1/4 xx 120` | |
`= 30` |
`=> C`
The eye colours of a sample of children were recorded.
When analysing this data, which of the following could be found?
`C`
`text(Eye colour is categorical data)`
`:.\ text(Only the mode can be found)`
`=> C`
A newspaper states: ‘It will most probably rain tomorrow.’
Which of the following best represents the probability of an event that will most probably occur?
`C`
`text(Probably) =>\ text(likelihood > 50%)`
`text(However 100% = certainty)`
`:.\ text(80% is the answer)`
`=> C`