The number of phone calls per,u+sg usptj2fpi-x. .ws( (z lkve0y, hour that store managers receive during the day are(p suws .. t2l(xpz+-,yj 0vifksg ,eu shown below.
$\begin{array}{llllllll}3 & 5 & 6 & 2 & 4 & 7 & 4 & 9\end{array} $
1. Find the median number of calls.   
2. Write down the value of
(1). the mode;   
(2). the upper quartile.   
3. Find the probability that managers received no more than 5 calls in a randomly chosen hour.   

  The number of days rain per month in London varies jpy-ul:f29rv( it/arn+8u(5 klm jiedepending on the time of year. The 9fy 2p5 eil a/( kv8jmurtun(-+j:i lrdata shows the number of wet days per month. $\begin{array}{llllllllllll}17 & 13 & 11 & 14 & 13 & 11 & 13 & 12 & 13 & 14 & 16 & 16\end{array}$
1. For this data, find
(1). the median;   
(2). the minimum and maximum values. min =    max =   

The lower quartile of the data is 12.5 and the upper quartile of the data is 15 .
2. Draw a box-and-whisker diagram to represent the data.

  Aaron lives in a remote country town in outback Australia. He uses Amazon.coz9.sbh:veafr 6 1) gdtkoqa 9:m to purchase everyday supplies. ga )dsa6k:h.vbr qfotz1e 99:Due to his remote location, it can take numerous days for deliveries to arrive. Aaron records the number of days for an order to arrive on his next ten orders, with the results as follows.

4,5,3,2,6,11,4,4,6,7


For this data set, find the value of
1. the median;   
2. the mean;   
3. the standard deviation.   

  The number of weeks spent in a hospital by a sample of lung cancer patiesqu:x)bvkr3 u8l;2a7v/ux cys 7y( upnt during as7r)a(byl8k2uquxvy;c / : u3ps7vux course of chemotherapy treatment was recorded. The data is illustrated in the box-and-whisker diagram shown below.



1. For this data, write down
(1). the maximum number of weeks spent during a course of treatment.    weeks
(2). the upper quartile.    weeks
(3). the median.    weeks

Dr. Buckley interprets this box-and-whisker diagram and claims that the percentage of patients spending less than 13 weeks during a treatment is less than the percentage of those who spend more than 25 weeks.
2. State whether Dr. Buckley's interpretation is correct. Justify your answer.

  An analyst working at the Shanghaiw3lfc+f t,4j o shipping port conducts a study on the port wait tiflf jc+w3, to4mes of shipping containers for a particular month. The analyst creates a box-and-whisker diagram to represent the time, in hours, containers spend in the port. The diagram is shown below.


1. Using the box-and-whisker diagram, write down
1. the minimum number of hours a container spent in the port.    hours
2. the lower quartile.    hours
3. the upper quartile.    hours

Using the box-and-whisker diagram, the analyst claims that the percentage of containers spending more than 23 hours in port is higher than the percentage of containers spending less than 23 hours in port.
2. State whether the analyst is correct. Justify your answer.

  The column graph below shows the number of wet days per week recorded for a pdhaov *k8f 8z3;v q9gferiod of time in Melbogz8*39h qfvfk ;dvo 8aurne, Australia.


1. Write down how many weeks were recorded.   
2. Write down the modal number of wet days per week.
3. Calculate the mean number of wet days per week.   
4. Determine the percentage of weeks which had more than 2 wet days.    %

  The lifetime, in thousand of hours, of LED bulbs hah,vo);a,jn9k mebm,cgo/,at a manufacture plant were recorded for a periodic quality check. The data is illustrated in the box-and-whisker diagram shown bm ; b ,hohmkov)/aj,ecgna9 ,,elow.


1. Write down the median lifetime of these LED bulbs.    hours
2. Write down the upper quartile.    hours
3. Find the interquartile range.
The lifetimes of these LED bulbs are normally distributed.   
4. Find the longest lifetime of an LED bulb that is still not considered an outlier.   

  Peter owns a diary farm in New Plymouth, New Zealand, where hundro phm/ yifwp jxm:/*b1,b6p6heds of cows are bred for milk. In an effort of evalua bbp jhm:pow 6/fx1*p/yh6im ,ting the cows productivity, he recorded the amount of milk that the cows produce over several days. The following box-and-whisker diagram represents the summary of the data.



1. Write down the median amount of milk that a diary cow produces per day at his farm.    liters per day
2. Write down the lower and upper quartiles. $Q_1$   liters per day $Q_2$    liters per day
3. Find the interquartile range.
The amount of milk that these cows produce each day is known as being normally distributed.   
4. Find the lowest amount of milk that a cow can produce and still not be considered an outlier.

The manager of a smal9epj;nxpo .n;0w l8s( pk4rmrl movie theatre recorded the number of tickets purchased each day for 14 days. The number of tickets purchased.n rs9xo0lppe;;8jnrwm p4(k each day were:
31,36,37,17,25,27,32,54,37,21,19,26,26,29
For these data, the lower quartile is 25 and the upper quartile is 36 .
1. Show that the value 54 would be considered an outlier.

The box and whisker diaaram for tickets purchased is aiven below.



The manager of a second small theatre also recorded the number of tickets purchased for the same 14 days, giving the following box and whisker diagram:


The manager of the second theatre claims that, in general, his theatre has more customers than the first theatre.
2. By comparing the two box and whisker diagrams, give one piece of evidence that supports this claim and one that may refute it.

  The following table shows the number of)i ydt1oqbw; o0b(8qb overtime hours worked by employees in a company. q1oibyw0 )otq(8b d b;

It is known that the mean number of overtime hours is 1 .
1. Find the value of x .   
2. Find the standard deviation of the data. ≈   

  The distribution of tomato sales in a grocek(apwzc t50- jry store over 100 days is displayed in the followkj0(a w5pczt- ing box-and-whisker diagram.



1. Write down the median tomato sales.    kg
2. Write down the minimum tomato sales.    kg
3. Find the interquartile range.   
4. Write down the number of days the tomato sales will be
(1) between 42 $\mathrm{~kg}$ and 50 $\mathrm{~kg}$ ;   
(2) between 26 $\mathrm{~kg}$ and 55 $\mathrm{~kg}$ .   
Another day's sales were recorded. It was a very quiet day due to bad weather and only 8 \mathrm{~kg} of tomatoes were sold.
5. Determine if this day would be considered an outlier.

  The following cumulative frequency diagram shows tygxfh t c- 7rvl5u+;9phe lengths of 80 pieces of string, intr pg5lcy;vu7f+x h9- cm.



1.Find the median length.
The following frequency table also gives the lengths of the 80 pieces of string.


2.(1)Write down the value of q.   
(2)Find the value of p.   

  The cumulative frequency curve below shows t iwjukz4us7o: 1pwj*-:6g bn w:m 5trwm3qz;t he number of hours spent by 60 students on their IBr mnup4:jqwsmt :w ;u wi3zbz j7-6wo5tg: *k1 homework during one week.



1. Write down the median value of this data. Give your answer correct to the nearest hour.    hours
2. The upper quartile of this data is 10.1. Find the interquartile range, giving your answer correct to one decimal place.   
3. The minimum number of hours spent by students on their homework is zero. The maximum number hours spent by students is 14 . Draw a box-and-whisker diagram to represent this data.
4. The 60 students sampled were chosen by randomly sampling 30 students from Diploma Program Year 1 and 30 students from Diploma Program Year 2. Both the Year 1 and Year 2 cohorts had the same number of total students. Write down the sampling method used.

  Uber, the ride sharing technology service, conducts a study of 80 of their dr4 f0:qn8ghttzivers in San Fransisco to determine how many kilometers they travel each month. The distance each driver travelled in April is recorde0zhfttqn:8 g4d. The cumulative frequency curve for this data is shown below.


1. Find the number of drivers that travelled a distance between 3200 and 5000 kilometres.   
2. Use the cumulative frequency curve to find the
(1) median distance;    km
(2) lower quartile;    km
(3) upper quartile.    km
3. Hence, find the interquartile range.   
4. Write down the percentage of drivers that travelled a distance greater than the upper quartile.
5. Find the number of drivers that travelled a distance less than or equal to 2750 $\mathrm{~km}$ .
t is known that 11 drivers travelled more than m kilometres.    %
6. Find the value of m .
The smallest distance travelled by one of the drivers was 500 $\mathrm{~km} $. The longest distance travelled by one of the drivers was 6000 $\mathrm{~km} $.   
7. On graph paper, draw a box-and-whisker diagram for these data. Use a scale of $2 \mathrm{~cm$} to represent 1000 $\mathrm{~km}$ .

  Two groups of 60 students each were asked how many movies they ha5vwn5* vvhqo)tw42b5btis gqgmn : xk727eh)ve watched in the last month.The results for the fitv x v7g qq 4k72*)5h)tnewmiogb: hvn5bsw25rst group are shown in the following table.


The quartiles for these results are 4 and 6 .
1. Determine down the value of the median for these results.   
2. Draw a box-and-whisker diagram for these results on the following grid.



The results for the second group are shown in the following box-and-whisker diagram.



3.Estimate the number of students in the second group who have watched at least 7 movies.   

  A market research survey asked 200 jx w 8 66oo1qaqbqwr36lx3f; hteenagers for the number of minutes they spend on their phones on a daily basis. The results were recorded in the following bo63olbw haq3r q8jwq;o61 xxf6x-and-whisker diagram.


1. Write down the median.
The following incomplete table shows the distribution of the responses from these 200 teenagers.    minutes



2. Complete the table.
3. (1) Write down the mid-interval value for the $80 
(2) Using the table, calculate an estimate for the mean number of minutes spent on phones daily by these 200 teenagers. ≈    minutes

The 200 teenages were chosen for the survey by randomly selecting student ID numbers in a school, using a random number generator.
4. Identify the sampling method used.

  250 households in a town were surveyed awsr*8 18 cwjmp;zs p7osking how many video streaming services the household subscribes to. The outcome of the surv8*w8crmsjs 1pp oz; w7ey is shown in the following table.



1. Find the number of households that subscribe to more than 2 services.   
2. Find the modal number of streaming services per household.
3. From the data, find
(1) the median number of streaming services;
(2) the lower quartile;
(3) the upper quartile.
A different survey conducted by an entertainment blog asked 150 survey participants of their preference between two video streaming services; Netflix and YouTube TV. The results of this survev data is summarized in the followina table



A $\chi^{2}$ test of independence is carried out at the 10 \% significance level.
4. State
(1) the null hypothesis;
(2) the alternative hypothesis.
5. Write down the number of degrees of freedom for this test.   
6. Calculate the expected number of people between 30--45 that prefer Netflix. ≈   
7. Find the p value for this test.≈   
8. State the conclusion for this test.

  The following cumulative frequency diagram shows the distance upmmw o d -9mf,49tb)bz*l,zc students need to travel to get tomf,mz9b9pu, -m*)z4lodct w b school.



1. Find the median distance a student travels to school.   
2. Find the number of students that travel between 2 $\mathrm{~km}$ and 4 $\mathrm{~km}$ to get to school.   
3. Find the percentage of students that travel more than 4.5 $\mathrm{~km}$ to get to school.    %

  At the end of a working day, a sur4s*(nwlzenk70 ot* ol 31k mhjeb12phvey was conducted at a company head office asking employees how frmohh *2op z(b 7n*nwltelj 0k11es 43kequently they take sick leave days per year.

The data is shown in the following table.


1. State whether the data is discrete or continuous.

The mean number of sick leave days per year is 4 .
2. Find the value of k .

In this survey, these employees were arranged in alphabetical order and every 5th person was asked for the number of sick leaves per year.   
3. Identify the sampling technique used in the survey.

  John decided to build a stone fence around his hous)nn 23cgh oei4h 5i) 1x z/jaji8cmhn(e and lay a stone walkway. John ordered a large bag of stones and first chose a random a sample of 50 stones for measuring. He measured the diameters of the stones correct to the nearest centimetre. The following table shows the frequency distribuna(4hcghxn cz253 8 h ime1ji)/jo)n ition of these diameters.


1. Find the value of (1) the mean diameter of these stones; ≈    cm
(2) the standard deviation of the diameters of these stones.
John assumes that the diameters of all the stones from this bag are normally distributed with a mean 16 $\mathrm{~cm}$ and a standard deviation of 1.1 $\mathrm{~cm}$ John sorts all stones by their diameter size.≈    cm

2. John selects the largest stones, with diameters of 18 $\mathrm{~cm}$ or greater, to use for the stone walkway. Estimate the percentage of stones used.≈    %
3. John selects small stones, which have a diameter less than x $\mathrm{~cm} $ to use for a walkway border. The small stones account for 5 $\%$ of the total number of stones. Calculate the value of x .
4. John selects medium stones to use the stone fence. Estimate the percentage of medium stones with diameter more than x $\mathrm{~cm}$ from part (c) and less than 18 $\mathrm{~cm}$ .≈    %
5. John estimates that there are about 10000 stones in total. Estimate the number of large stones.   

  The table below shows the time, in minutes, taken to complete a Statistics tem4i5tve ;a(b7qybn2wst v qw(mat;e bib27n45yby a group of 100 students.



1. Write down the value of x .   
2. Use the time interval midpoints to estimate the average time taken to complete the test. The time taken to complete the test is displayed on the cumulative frequency graph below.    minutes



3. Estimate the median time of test completion.    minutes
4. Estimate the number of students that spend at least 30 minutes on the test.   
5. Calculate the interquartile range.   
6. Draw a box-and-whisker diagram for this data.
7. Determine if a student who takes 5 minutes to complete the test would be considered an outlier.(a,b) a=   b=  

  During the recent English Premier Leagy+ +(wonyym.bi (n:a,/*zl qt,fnr ah elgs+1ue football season, the number of matches in which a certain number of goals were scored were recorded inylmn1+n+w. l+y(/zho,,inf b(ar *y:sat q ge the table below. For example, there were 18 matches where 5 goals were scored.



The lower quartile for these results is 2 , and median is 3 .
1. Write down the value of the upper quartile for these results.
2. Draw a box-and-whisker diagram for these results.
3. Find the probability that, in a randomly chosen match, the number of goals will be less than the upper quartile. Give your answer correct to two decimal places. ≈   

  The histogram below shows the weights of 40 Honeydew Melh+6ek1llo) z pd ;p9lcons, each measured correct to the o+zh 9;epkl1p6)c lldnearest kg.


1. Write down the modal weight of the melons.    kg
2. Find the median weight of the melons.
The lower quartile is 3 $\mathrm{~kg}$ .    kg
3. Calculate
(1) the upper quartile;    kg
(2) the interquartile range.   

  The histogram below showsgav mf)ey9sk6 qr.qk g 25c*mo-sj 1m. the number of working hours recorded by 145 employees in a company during a particular week, each measuresyf2smkja.1oqqg-) k6 mrmg5* 9. ecvd correct to the nearest hour and then rounded to the nearest units of 10 hours.


1. Write down the modal working time of the employees.    hours
2 . Find the median working time.
The upper quartile is 50 working hours.    hours
3. Calculate
(1) the lower quartile;    hours
(2) the interquartile range.   

  The cumulative frequency curve below syxz s. l,ci kd9,p7v;k c;q:wpm4qw:xhows the serving speed, in km/h, of a sample of 80 randomly chosen serves by Roger Federer, the famolki .9c4: x w;;,qycsxzpv,pqmdw: k7us Swiss professional tennis player.



Give your answers to the following correct to the nearest whole number, wherever applicable.
1. Estimate the minimum and maximum speeds of these serves. min =    km/h max =    km/h
2. Estimate the median speed of these serves.   km/h
3. Estimate the lower and upper quatiles. $Q_1$ =   km/h $ Q_2$ =   km/h
4. Calculate the interquartile range.   
5. Estimate the number of serves that had speed of more than 215 $\mathrm{~km} / \mathrm{h}$ .   

The table below shows speeds of these serves.




6. Find the values of x and y . x =    y =   
7. Write down
(1) the modal class;
(2) the mid-interval value of the modal class.   
8. Estimate the below using your Graphic Display Calculator.
(1) the mean speed of these serves;    km/h
(2) the standard deviation.    km/h
9. Estimate the percentage of the serves where the serving speed differs from the mean by no more than 20 $\mathrm{~km} / \mathrm{hr}$ .    %

  A group of iPhone users participated in av (s y t 1x-mkvr;xyx,wmxv-z1+7wob . research survey and the ages of participants were recorded ,xmvzb-1xoy(7tvwkw1v ;.+r -mxyxs in the following table.


It is known that 561. Write down
(1) the modal class;
(2) the mid-interval vaue of the modal class.   
2. Determine the class in which the lower quartile lies.
3. Calculate the average age of participants between the ages of 45 and 74 .

The participants in this survey were chosen by randomly selecting people walking past a stand in a shopping mall. However, to be polite, the surveyor only asked people who were by themselves and looked to not be in a hurry.≈   
4. Write down the type of sampling method used.

  The table below shows the distribution of the number of fmx 0j- )nnx.3 vxmc ayp/:m8rnish caught during a fishing contest by 100 contn . xxymn:jam-)03mpr /c8 nvxestants.



1. Calculate
(1) the mean number of fish caught by a contestant;≈   
(2) the standard deviation. ≈   
2. Find the median number of fish caught in the contest.   
3. Find the interquartile range.   
4. Determine if a contestant who caught 10 fish would be considered an outlier.

One of the contestants is chosen at random.(a,b) a=   b=  
5. Find the probability that this chosen contestant caught 6 fish or more.

A second contestant is randomly chosen.   
6. Given that the first contestant caught 6 fish or more, find the probability that each of these two contestants caught exactly 7 fish.

The cost of the fishing equipment used by the 100 contestants is normally distributed with a mean of 1200 US Dollars (USD) and a standard deviation of 300 USD. ≈   
7. (1) Calculate the probability that a contestant chosen at random spent at least 1000 USD for fishing equipment. ≈   
(2) Calculate the expected number of contestants that spent at least 1000 USD on fishing equipment.   

  The table below shows the distributiono) ql2j qg jk1(rwp89hu/gn be6/nj5q of trip numbers made by a group of 100 taxi drivers surveyed on a workie6kj 2qwj 9jb1 5/noqqpu/glngh)8r (ng day in Sydney.




1. Find
(1) the mean number of trips made by the taxi drivers; ≈   
(2) the standard deviation of the number of trips made.≈   
2. Find the median number of trips made by taxi drivers.   
3. Find the interquartile range.

A taxi driver is chosen at random from the group of 100 taxi drivers.   
4. Find the probability that this taxi driver made 13 or more trips.

A second taxi driver is chosen at random from the group of 100 taxi drivers.   
5. Given that the first taxi driver chosen at random made 13 or more trips, find the probability that both taxi drivers made 14 trips.

The amount of time that the 100 taxi drivers waited for their next client was normally distributed with a mean of 15 minutes and a standard deviation of 4 minutes.≈   
6. (1) Calculate the probability that a taxi driver chosen at random waited at least 12 minutes for the next client.≈   
(2) Calculate the expected number of taxi drivers that waited at least 12 minutes for their next client.

The 100 taxi drivers were selected for the survey by ordering taxi identification numbers in ascending order, then selecting every 10 th number.   
7. Identify the sampling technique used in this sampling method.