Statistics

\(\begin{aligned}
&\text{The frequency table summarizes the 57 data values in a data set. What is the maximum}\\
&\text{data value in the data set?}\end{aligned}\)

\(\begin{aligned}
&\text{The bar graph shows the distribution of 419 cans collected by 10 different groups}\\
&\text{for a food drive. How many cans were collected by group 6?}\\
\end{aligned}\)

\(\begin{aligned}
&\text{The table summarizes the UV index value recorded by a research assistant at noon}\\
&\text{each day for 49 days.}\\&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\begin{array}{|c|c|}\hline\text{ UV index}&\text{Number of days}\\\hline1&9\\\hline2&15\\\hline3&12\\\hline4&13\\\hline\end{array}\\\\
&\text{According to the table, a UV index value of 1 was recorded on how many days?}\end{aligned}\)

\(\begin{aligned}
&\text{The table shows the frequency of each value in a data set.}\\\\
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\begin{array}{|c|c|}\hline\text{Value}&\text{Frequency}\\\hline120&3\\\hline130&8\\\hline140&18\\\hline150&8\\\hline160&1\\\hline\end{array}\\\\&\text{What is the minimum value of the data set?}\end{aligned}\)

\(\begin{aligned}&\text{To study the characteristics of sea stars in a group of tide pools, researchers }\\
&\text{measured the diameter of the sea stars within the tide pools. The dot plot gives}\\&\text{the diameter, to the nearest inch, of each of the sea stars in these tide pools.}\end{aligned}\)

\(\begin{aligned}
&\text{Based on the dot plot, how many sea stars had a diameter, to the nearest inch,}\\
&\text{of 16 inches?}\end{aligned}\)

\(\begin{aligned}
&\text{The dot plot shows the estimated market values for 15 houses in a neighborhood. What is}\\
&\text{the maximum estimated market value, in thousands of dollars, for the data set?}\end{aligned}\)

\(\begin{aligned}
&\text{The dot plot shown gives the distribution of values in a data set. What is the minimum value}\\
&\text{in the data set ?}\end{aligned}\)

\(\begin{aligned}
&\text{A group of students voted on five after-school activities. The bar graph shows the number of}\\
&\text{students who voted for each of the five activities. How many students chose activity 3?}\end{aligned}\)

\(\begin{aligned}
&\text{The bar graph summarizes the charge, in kilowatt-hours (kWh), a battery }\\
&\text{received each day for 15 days.}\end{aligned}\)

\(\text{For how many of these 15 days did the battery receive a charge of 0 kWh?}\)

\(\begin{aligned}
&\text{A store owner recorded the number of units of a certain product that }\\
&\text{were sold per day for 28 days. What is the minimum number of units of}\\&\text{this product sold per day for these 28 days?}\end{aligned}\)

\(\begin{aligned}
&\text{The bar graph shows the number of trees planted for 4 separate plots of land on a tree}\\
&\text{farm.}\end{aligned}\)

\(\text{What is the maximum number of trees planted on one of these 4 plots of land?}\)

\(\text{The bar graph shows the frequency of each data value in a data set.}\)

\(\text{What is the frequency of data value 2 in this data set?}\)

\(\begin{aligned}
&\text{A list of 10 data values is shown.}\\\\
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~6,8,16,4,17,26,8,5,5,5\\\\
&\text{What is the mean of these data?}\end{aligned}\)

\(\begin{aligned}
&\text{Each value in the data set shown represents the height, in centimeters, of a plant.}\\\\
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~6,10,13,2,15,22,10,4,4,4\\\\
&\text{What is the mean height, in centimeters, of these plants?}\end{aligned}\)

\(
\begin{aligned}&\text{The list gives the mass, in grams, of 5 ruffed lemurs.}\\\\
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text{3,910; 3,910; 3,130; 3,950; 3,150}\\\\&\text{What is the mean mass, in grams, of these 5 ruffed lemurs?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\begin{array}{|c|c|}
\hline&\text{Time}\\
\text{Task}&\text{(minutes)}\\\hline
\text{A}&8\\\hline\text{B}&6\\\hline\text{C}&14\\\hline\text{D}&11\\\hline\text{E}&11\\\hline\end{array}\\\\&\text{The table shows the amount of time it took a participant in a study to complete each of 5}\\&\text{tasks. What was the mean time, in minutes, for this participant to complete a task?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~700,1200,1600,2000,x\\\\
&\text{If the mean of the five numbers above is 1600, what is the value of }x?\end{aligned}\)

\(\begin{aligned}
&\text{The mean score of 8 players in a basketball game was 14.5 points. If the highest}\\
&\text{individual score is removed, the mean score of the remaining 7 players becomes}\\&\text{12 points. What was the highest score?}\end{aligned}\)

\(\begin{aligned}
&\text{A survey of the daily commuting times, in minutes, of seven different Chicago-based}\\
&\text{employees at a certain company yielded a data set consisting of the values 32, 14, 44, 31, 51,}\\
&\text{24, and 44. A survey of the daily commuting times, in minutes, of seven different San}\\
&\text{Francisco-based employees at the same company yielded a data set consisting of the values}\\
&46,32,19,34,48,x,\text{and }38.\text{ If the means of the two data sets are equal, what is the value of }\\&x?\end{aligned}\)

\(\begin{aligned}
&\text{Andrew and Maria each collected six rocks, and the masses of the rocks are shown in the table }\\
&\text{above. The mean of the masses of the rocks Maria collected is 0.1 kilogram greater than the }\\
&\text{mean of the masses of the rocks Andrew collected. What is the value of }x?\end{aligned}\)

\(\begin{aligned}
&\text{Data set A consists of the heights of 75 buildings and has a mean of 32 meters. Data set B }\\
&\text{consists of the heights of 50 buildings and has a mean of 62 meters. Data set C consists of}\\
&\text{the heights of the 125 buildings from data sets A and B. What is the mean, in meters, of}\\&\text{data set C?}\end{aligned}\)

\(\begin{aligned}&\text{An environmental scientist is investigating the volatility of 175 organic compounds by}\\&\text{finding the boiling point of each compound. The mean boiling point of all 175}\\&\text{compounds is 167 degrees Celsius. The scientist classifies each of these compounds as}\\&\text{either semivolatile or volatile. Of the 175 compounds, 50 compounds were classified as}\\&\text{semivolatile, and these 50 compounds have a mean boiling point of 327 degrees}\\&\text{Celsius. The remaining 125 compounds were classified as volatile. What is the mean}\\&\text{boiling point, in degrees Celsius, of the 125 compounds classified as volatile}\\&\text{compounds?}\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text{Data set X: 5, 9, 9, 13}\\&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text{Data set Y: 5, 9, 9, 13, 27}\\\\
&\text{The lists give the values in data sets X and Y. Which statement correctly compares  }\\
&\text{the mean of data set X and the mean of data set Y?}
\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\begin{array}{|c|c|c|}\hline\text{}&\text{Data set A}&\text{Data set B}\\\text{Value}&\text{frequency}&\text{frequency}\\
\hline40&2&8\\\hline43&4&7\\\hline46&5&5\\\hline49&7&4\\\hline52&8&2\\\hline\end{array}\\\\
&\text{Data set A and data set B each consist of 26 values. The table shows the frequencies of the}\\&\text{values for each data set. Which of the following statements best compares the means of}\\&\text{the two data sets?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~\begin{array}{|c|c|c|c|c|}\hline\text{}&\text{Data set A}&\text{Data set B}&\text{Data set C}&\text{Data set D}\\\text{Values}&\text{frequency}&\text{frequency}&\text{frequency}&\text{frequency}\\\hline40&0&0&8&8\\\hline43&2&3&3&4\\\hline46&4&3&3&2\\\hline49&8&8&0&0\\\hline\end{array}\\\\
&\text{The table shows the frequencies of the data values for four data sets. Which data set has the}\\
&\text{greatest mean?}\end{aligned}\)

\(\begin{aligned}&\text{Each of the following frequency tables represents a data set. Which data set has the}\\&\text{greatest mean?}\end{aligned}\)

\(\begin{aligned}&\text{Five }Eretmochelys~imbricata,\text{ a type of sea turtle, each have a nest. The table }\\
&\text{shows an original data set of the number of eggs that each turtle laid in its nest.}\\\\
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\begin{array}{|c|c|}\hline\text{Nest}&\text{Number of eggs}\\\hline\mathrm{A}&149\\\hline\mathrm{B}&144\\\hline\mathrm{C}&148\\\hline\mathrm{D}&136\\\hline\mathrm{E}&139\\\hline\end{array}\\\\
&\text{A sixth nest with 121 eggs is added to create a new data set. Which of the}\\&\text{following correctly compares the means of the two data sets?}
\end{aligned}\)

\(\begin{aligned}
&\text{Two data sets of 23 integers each are summarized in the histograms shown. For each of }\\
&\text{the histograms, the first interval represents the frequency of integers greater than or}\\
&\text{equal to 10, but less than 20. The second interval represents the frequency of integers}\\
&\text{greater than or equal to 20, but less than 30, and so on. What is the smallest possible} \\
&\text{difference between the mean of data set A and the mean of data set B?}\end{aligned}\)

\(\begin{aligned}&\text{Data sets X and Y are summarized in the tables shown, where }a,b,\text{ and }c\text{ are positive,}\\&\text{consecutive integers and }a < b < c.\text{ Which statement comparing the means of the data sets}\\&\text{is true?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~73,74,75,77,79,82,84,85,91\\\\&\text{What is the median of the data shown?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~13,17,23,6,4,8,17,15,16\\\\
&\text{The list gives the low temperatures, in degrees Fahrenheit, for 9 days in December in a}\\
&\text{certain city. According to the list, what is the median low temperature, in degrees}\\
&\text{Fahrenheit, for these 9 days?}\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text{Data set A: 2, 2, 2, 5, 5, 8, 11, 11, 14, 14, 14}\\
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text{Data set B: 2, 5, 5, 8, 8, 8, 8,11, 11, 11, 14}\\\\
&\text{Data set A and data set B each have 11 values. Which of the following statements best}\\
&\text{compares the median of data set A and the median of data set B?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\begin{array}{|c|c|}\hline\text{Number of}&\text{Number of}\\\text{queen ants}&\text{colonies}\\\hline1&11\\\hline2&9\\\hline3&7\\\hline4&6\\\hline5&6\\\hline\end{array}\\\\
&\text{Scientists collected acorns that each housed a colony of a particular species and then analyzed}\\
&\text{each colony’s structure. For these colonies, the table summarizes the number of queen ants}\\
&\text{per colony. For these colonies, what is the median number of queen ants per colony?}\\
\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\begin{array}{|c|c|}\hline\text{Number of birds}&\text{Number of days}\\\hline14&3\\\hline15&3\\\hline16&4\\\hline17&1\\\hline18&3\\\hline19&9\\\hline\end{array}\\\\
&\text{A science class studied the feeding behavior of the birds that visited a bird feeder each}\\
&\text{school day for a period of time. The table summarizes the number of birds the class}\\&\text{observed visiting the bird feeder each school day during this period of time. What is the}\\&\text{median number of birds the class observed visiting the bird feeder each school day during}\\&\text{this period of time?}\end{aligned}\)

\(\begin{aligned}
&\text{The table shown summarizes the number of employees at each of the 17 restaurants }\\&\text{in a town.}\end{aligned}\)

\(\begin{aligned}&\text{Which of the following could be the median number of employees for}\\&\text{the restaurants in this town?}\end{aligned}\)

\(\begin{aligned}
&\text{The table shows the distribution of height, in centimeters, of 25 objects.}\\\\
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\begin{array}{|c|c|}\hline\text{Height}&\text{Frequency}\\\hline\text{0 to 100}&8\\\hline\text{101 to 200}&6\\\hline\text{201 to 300}&5\\\hline\text{301 to 400}&4\\\hline\text{401 to 500}&2\\\hline\end{array}\\\\&\text{Which of the following could be the median height of these objects?}\end{aligned}\)

\(\begin{aligned}&\text{The frequency table summarizes a data set of the weights, rounded to the nearest pound, of}\\&\text{71 tortoises. A weight of 39 pounds is added to the original data set, creating a new data set}\\&\text{of the weights, rounded to the nearest pound, of 72 tortoises. Which statement best compares}\\&\text{the mean and median of the new data set to the mean and median of the original data set?}\end{aligned}\)

\(\begin{aligned}
&\text{A data set of the orbital periods, rounded to the nearest whole number of Earth days for}\\
&\text{13 of Jupiter’s moons is represented in the dot plot. An additional moon with an orbital}\\
&\text{period of 628 days is added to the original data set to create a new data set of 14 orbital}\\
&\text{periods. Which statement best compares the mean and median of the new data set to the}\\
&\text{mean and median of the original data set?}\end{aligned}\)

\(\begin{aligned}&\text{Data set F consists of 55 integers, where the value of each integer is between 150 and 260.}\\&\text{Data set G consists of the same 55 integers in data set F as well as the integer 10. Which of}\\&\text{the following must be less for data set G than for data set F?}\\\\&~~~~~~~\text{ I. The mean}\\&~~~~~~\text{ II. The median}\end{aligned}\)

\(\begin{aligned}&\text{The histogram summarizes a data set of the weights, in pounds, of 14 salmon. If an}\\&\text{additional weight of 85 pounds is added to the original data set to create a new data set of 15}\\&\text{weights of salmon, which of the following measures must be greater for the new data set}\\&\text{than for the original data set?}\\\\
&~~~~~~\text{ I. The median}\\
&~~~~~\text{ II. The mean}\end{aligned}\)

\(\begin{aligned}&\text{The histogram summarizes data set A, which represents the number of points per player }\\
&\text{earned by 50 players of a game. A new player earns 18 points playing the game,}\\&\text{and this number of points is added to data set A to create data set B with 51 values.}\\&\text{Which of the following must be true?}\\\\
&~~~~~~~~~\text{I. }\text{The median number of points per player for data set B is less than}\\
&~~~~~~~~~~~~\text{ the median number of points per player for data set A.}\\\\&~~~~~~~~\text{II. }\text{The mean number of points per player for data set B is less than}\\&~~~~~~~~~~~~\text{ the mean number of points per player for data set A.}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~23,27,27,32,35,36,52\\\\&\text{What is the range of the 7 scores shown?}\end{aligned}\)

\(\begin{aligned}
&\text{The list gives the number of individuals in each of 6 groups of ring-tailed lemurs.}\\\\
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~17,4,20,17,18,6\\\\
&\text{What is the range of the numbers of individuals for the 6 groups of ring-tailed }\\&\text{lemurs?}\end{aligned}\)

\(\begin{aligned}&\text{The two box plots show the distribution of number of books read}\\&\text{over the summer by the students in two different English classes.}\\&\text{What is the positive difference between the ranges of number of}\\&\text{books read over the summer for the two classes?}\end{aligned}\)

\(\begin{aligned}
&\text{The dot plot represents the 15 values in data set A. Data set B is created by adding 56 }\\
&\text{to each of the values in data set A. Which of the following correctly compares the }\\
&\text{medians and the ranges of data sets A and B?}\end{aligned}\)

\(\begin{aligned}
&\text{Each of the dot plots shown represents the number of glue sticks brought in by each student }\\
&\text{for two classes, class A and class B. Which statement best compares the standard deviations }\\
&\text{of the numbers of glue sticks brought in by each student for these two classes?}\end{aligned}\)

\(\text{The values in data sets X and Y are shown in the table.}\)

\(\begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline\mathrm{Data}\\\text{set X}&13&13&14&14&15&16&16&17&17\\\hline\text{Data}\\\text{set Y}&2&2&3&3&4&5&5&6&6\\\hline\end{array}\)

\(\begin{aligned}&\text{The standard deviation of data set X is }q,\text{and the standard deviation of data set Y is }s.\text{ Which}\\&\text{of the following statements about the standard deviation of the data sets is true?}\end{aligned}\)

\(\begin{aligned}&\text{Each of the following frequency tables represents a data set. Which of these frequency tables}\\&\text{represents the data set with the smallest standard deviation?}\end{aligned}\)

\(\begin{aligned}&\text{The histograms summarize the distributions of scores for team A and team B. Which}\\&\text{statement best compares the standard deviations of scores for these teams?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text{Data set A: 8, 11, 12, 15, 21, 27}\\&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text{ Data set B: 9, 12, 13, 16, 22, }h\\\\&\text{Data sets A and B each consist of 6 values as shown, where }h\text{ is a constant. If the standard}\\&\text{deviation of data set A is greater than the standard deviation of data set B, which of the}\\&\text{following could be the value of }h?\\&~~~~~~\text{I. 23}\\&~~~~\text{II. 28}\\&~~~\text{III. 29}\end{aligned}\)

\(\text{The dot plots represent the distributions of values in data sets A and B.}\)

\(\begin{aligned}&\text{Which of the following statements must be true?}\\\\
&~~~~~~~~~\text{I. The median of data set A is equal to the median of data set B.}\\
&~~~~~~~~\text{II. The standard deviation of data set A is equal to the standard }\\&~~~~~~~~~~~~~\text{deviation of data set B.}\end{aligned}\)

\(\begin{aligned}
&\text{Ari examined a set of 86 plants. The lightest plant has a mass of 2.8 kilograms (kg) and}\\
&\text{the heaviest plant has a mass of 6.2 kg. Chihiro examined the same set of 86 plants and}\\
&\text{also an additional plant with a mass of 11.7 kg. Which of the following must be true about}\\
&\text{the set of plants that Ari examined and the set of plants that Chihiro examined?}\end{aligned}\)