The number of phone calls per hour that store managers receive durinhx hst3*u ndviyj; u68lr4 6sqis2,e+g the day are shown below. ht64l,sje6 ndqu328sri+uxi;v * s yh
$\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 depending on the t:glq 23dx.t0,xj,8llt yrdcp ime of year. The data shows the number of wet days per xd q,.r0 p:ttl3ly,xgcl28 dj 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 ussgxnuj/(g)dhff 9l4 x p pr; bfnonq )w632-v+es Amazon.com to purchase everyday supplies. Due to his remote location, it can take numerous days for deliveries to arrive. Aaron records the number of days for an order to arrivbnnphn-x)4 jp(v xw+f/sgql 92d6r)3f ;fguoe 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 +djras+bjsh 8:;ffx0vf :lw )spent in a hospital by a sample of lung cancer patient during a course of chemotherapy treatment was recorded. The data is )+s0 dahrfs+x l 8wb:jffj: v;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 Shangjleio w(4 83rn4w v,bbhai shipping port conducts a study on the port wait times of shipping containers for a particular month. The analyst creates a box-and-whisker diagram to represent the time, in hours, n (jrboiv84 b4 ,w3lewcontainers 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 iu-6 fmh i2t:iper week recorded for a period of time in Melbourne, : umihi6t-if2 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 e +ue ps 3pg,*yy+9ost,rip5jhours, of LED bulbs at a manufacture plant were recorded for a peru , 9e+yeop,ip yj5spg+s*3triodic quality check. The data is illustrated in the box-and-whisker diagram shown below.


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 faru3db6fg ubu,2 m in New Plymouth, New Zealand, where hundreds of cows are bred for milk. In an effort of evaluating the cows productivity, he recorded the amount of milk that the cows produce over several days. The following box-and-whisker diagram represents thedu b3,u62bfgu 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 small mo1qj+kt422b xbvhh up+ jbfeur,3/*btt98 p bq vie theatre recorded the number of tickets purchased each day for 14 days. The number of tickets purchased ea/9pb*bh+jqt 4b2 tb 2rebuh3fvqj k+1xt 8 up,ch 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 numberc)n ,kh/1a*m dp fop(qhh t:0j/ e.wgo7wow7d of overtime hours worked by employees in a company.nch foe (h: jk, dw/0/h*. 7)o1qopmt wpdw7ga

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 grocery store ove+y *htt*a 7tb4 fq..r m jfpcdbgko*4+r 100 days is displayed in the following box-and-whisker a bgjft *h m.o.4f4qkd *++ttc7py*brdiagram.



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 shof uj2z 2dh)6mlws the lengths of 80 pieces of stri2hmzfl d2 6uj)ng, in 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 cu f)y 6edorck/ s.,tb4irve below shows the number of hours spent by 60 students one6dciorsfty,bk)4 /. their IB 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 serv6p6*wyp n ;+xoxxt *jiice, conducts a study of 80 of their drivers in San Fransisco to determnpx+piw6o t *x jy;*6xine how many kilometers they travel each month. The distance each driver travelled in April is recorded. 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 have watched in t74 xigf 1)cnp qak(a0bhe last month.The results for the first group are shown in the folxp0) 4(qcbk nafa g1i7lowing 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 teenagersmx:g 6tg,m: 5ukmnsgl9gd 7y8 for the number of minutes they spend on their phones on a daily basis. The results were recs,ygmmg :d:nl65 89gmxt u7 gkorded in the following box-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 asking how many videz5jw4-hi* z:i kku97ypi7,8yma qkqco streaming services the household subscribes to. The 54zqz ii*kak jy hqm-wp77iy9 : k,uc8outcome of the survey 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 .c2qn b0mkp./ obx:tlshows the distance students need to travel to get to sc .x k0:l .n/2otpqbmbchool.



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 survey was conducted at a company head office a (:.xnbs6 xp9vfql3 yfsking employees how frequently they take sick leave days per yxfy 39:vqxp6n(l b.fsear.

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 dcg *8,npl-2x/xsptqds 0j*dfence around his house 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 follonx,ds 8dld/t pcp-*qxgsj0*2 wing table shows the frequency distribution 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 2ax+ zx/3/i8:7zp okzobpkr t to complete a Statistics test by a group of tar 23z+x8/p zob k/:p7izoxk100 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 League footbei3//p4 j ru)awwzaa :g1t c0yall season, the number of matches in which a certain number of goals were scored were recordeczr1:/e4t)a0y3u awgi/ap jw d in 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 weighi6p u0r:b5,yv: lmdtnl x50zats of 40 Honeydew Melons, each measured correct to thv mx56l ilrd 0uy:0an :zptb,5e nearest 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 shows the number of working hours recorded by 145 9 yc;5odfcw.ny+ i db*employees in a company during a particular week, each measured correct to the nearest hour and then rounded to tbid5*c9 nyd y;woc +.fhe 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 shows the servingqx:3 qitmr: /b )ab4im speed, in km/h, of a sample of 80 randomly chosen serves bym at3x)q:bmr4/i:ibq Roger Federer, the famous 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 usert.v-+ce,eu4jzngz )5 r42 qvk-t cr djs participated in a research survey and the ages of participants w -vr e45 ,uv.dzt2 r jtej-+qkc4z)cngere recorded 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 fish caught dd9 dfa; i4 idg1,h/awruring a fishing contest by 100 contestantwgf ri9/;14i d,a ddahs.



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 distribution of trip numbers maze0 ajlw 5/ba,e0o 2gdde by a group of 100 taxi drivers surveyed b0dw 5ze2o aj0a, le/gon a working 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.