A data set $X$ has five-number summary

$4,7,10,15,19$.

A new data set $Y$ is formed using $y=30-2x$.

A data set has lower quartile $20$ and upper quartile $x$, where $x>20$. The data value $50$ is being tested as a possible upper outlier.

A grouped frequency table summarizes the durations of telephone calls. The frequency in the interval $20\leq t<30$ is $p$. The estimated mean duration is $22$ minutes.

The cumulative frequency graph shows the waiting times, in minutes, of $120$ patients at a clinic.

A university has $1200$ science students, $800$ arts students and $500$ business students. Researchers want a sample of $125$ students. They set proportional targets for each faculty, email all students and accept the first volunteers until each target is filled.

Group A contains $20$ observations with mean $12$ and population standard deviation $3$. Group B contains $30$ observations with mean $18$ and population standard deviation $4$. The groups are combined.

A population data set contains $25$ values. Its recorded mean is $48.2$ and its recorded population variance is $16.0$. One value was recorded as $62$ but should have been $52$.

A conservation organization wishes to estimate the number of hours spent each month by volunteers in three nature reserves. The reserves have $250$, $400$ and $550$ registered volunteers respectively. A proportional stratified random sample of $96$ volunteers is selected.

The cycling times, $t$ minutes, of $40$ participants are summarized below.

A sensor recorded the daily number of litres of water used by a greenhouse as

$16,17,18,18,19,19,20,20,20,21,22,22,23,23,39$

For these data, $Q_1=18$ and $Q_3=22$. The final value is later found to have been entered incorrectly.

The cumulative frequency graph shows the operating lifetimes, in hours, of $100$ rechargeable batteries.

The box-and-whisker diagrams compare assessment scores for classes A and B. Class A has five-number summary $42,56,63,70,82$. Class B has non-outlying five-number summary $38,60,64,68,75$, with outliers at $91$ and $95$.

A set of salinity measurements, $x$, has mean $34.8$, population standard deviation $0.600$, lower quartile $34.4$, median $34.9$ and upper quartile $35.2$. A calibrated sensor reports

$y=1.02x-0.7$

The increases in height, $h$ cm, of $24$ seedlings are summarized below.

The numbers of minutes spent resolving $15$ technical-support cases are

$12,14,15,16,17,18,18,19,20,21,22,24,25,27,46$.

For these data, the calculator quartiles are $Q_1=16$ and $Q_3=24$.

At a city sustainability festival, researchers ask the first $360$ visitors to a recycling station to report their weekly household waste. Of these visitors, $144$ submit a form. Twelve respondents leave the waste question blank. The missing entries are recorded as zero, giving a reported mean of $8.50\ \text{kg}$ for all $144$ forms.

Two machines produce metal rods. Machine A produces $20$ rods with mean length $50$ cm and population standard deviation $2$ cm. Machine B produces $30$ rods with mean length $54$ cm and population standard deviation $3$ cm. The $50$ rods are treated as one population.

A population data set contains $24$ measurements with mean $18.5$. Its lower and upper quartiles are $15$ and $21$ respectively. One additional measurement, $x$, is added to the data set. The mean of the enlarged data set is $19.2$.

A laboratory records the operating lives of $12$ prototype batteries. The recorded mean is $48.5$ hours and the recorded population standard deviation is $4.20$ hours. During a review, one recorded value of $59$ hours is found to be a transcription error; the correct value is $50$ hours. The prototypes were supplied by engineers who volunteered to participate in the study.

The masses, in kilograms, of discarded material collected from households are summarized in a grouped frequency table. The class intervals are $0\leq m<10$, $10\leq m<20$, $20\leq m<30$ and $30\leq m<40$, with respective frequencies $4$, $p$, $10$ and $6$. The estimated mean mass is $20.0$ kg.

A hospital has an ordered list of $960$ staff members. A researcher plans to select $80$ staff members using a systematic sample. The list consists of $80$ blocks of $12$ roster positions. In each block, one specified position is occupied by a night-shift worker; assignments at all other positions may vary between blocks. The hospital employs $480$ day-shift staff, $300$ evening-shift staff and $180$ night-shift staff.

A council asks $200$ randomly selected residents to rate a new public park on a scale from $0$ to $10$. There are $150$ responses, with a total score of $780$. A spreadsheet replaces each of the $50$ missing responses by $0$ and reports a mean score of $3.90$. The council believes every missing score, if known, would lie between $4$ and $8$ inclusive.

Two machines fill bottles with juice. Their five-number summaries, in millilitres, are shown below.

Machine A: $48,50,52,55,59$

Machine B: $45,51,54,57,60$

A separate test bottle contains $70$ ml.

Two statistical software packages use different quartile conventions for the same short data set. Package P reports $Q_1=8$ and $Q_3=14$. Package Q reports $Q_1=8.5$ and $Q_3=15$. The data set contains an observation of $24$.

A measuring instrument is tested on the same eight reference components on two occasions. On the first occasion, the readings have mean $100.4$ units and population standard deviation $1.20$ units. Every second-occasion reading is exactly $2.00$ units greater than its corresponding first-occasion reading. The certified value for each component is close to $100$ units.

An international organization compares monthly household energy costs. In Country A, the mean cost is $42000$ local currency units with population standard deviation $8000$. The conversion to a common unit is $y=0.025x$. In Country B, the reported mean is $1100$ common units with population standard deviation $150$ common units. Country A records taxes in the cost, while Country B excludes taxes.

The number of defects found on a component takes the values $0$, $1$, $2$, $3$ and $4$. Their respective frequencies are $3$, $5$, $k$, $4$ and $2$. The mean number of defects is $1.90$. The quality score is defined by $q=10-3x$, where $x$ is the number of defects.

The number of faults, $x$, found in each of $25$ manufactured panels is summarized below.

The mean number of faults is $2$.

A box plot for a data set $X$ has non-outlying five-number summary

$8,12,17,23,31$

Two additional values, $-8$ and $40$, are plotted separately. A transformed data set is defined by $y=100-3x$.