In a class survey, \(3\) of \(12\) students chose chess. What fraction of the students chose chess? Simplify it.

Eight out of \(20\) students walked to school. What percent walked?

In Class A, \(8\) of \(10\) students brought lunch. In Class B, \(8\) of \(20\) brought lunch. Which class had the greater share of students bringing lunch?

The table shows buttons that a class sorted by color. What is the relative frequency of red buttons? <table><tr><th>Color</th><th>Count</th></tr><tr><td>Blue</td><td>4</td></tr><tr><td>Red</td><td>3</td></tr><tr><td>Green</td><td>3</td></tr></table>

The graph shows the relative frequencies of students' favorite after-school clubs. Which club was chosen by half the students?

The circle graph shows students' club choices. What fraction of the students chose Chess?

A computer analyzes an English-language news article containing \(400\) letters. The letter E appears \(52\) times, N appears \(28\) times, and Q appears once. a) Find the relative frequencies of E, N, and Q. Give each result as a percent. b) A reference model for this activity uses \(12.7\%\) as the long-run proportion of E in English text. Compare your result from part a with this value and give one possible reason for the difference.

A survey of \(200\) students found their favorite activities: sports (\(80\)), music (\(50\)), gaming (\(40\)), and reading (\(30\)). Lucas says, “Four activities means each must make up \(25\%\) of the answers.” a) Explain the mistake. b) What percent of students chose reading? c) What percent chose sports or music?

A factory packs LED bulbs in boxes of \(20\). A quality check recorded the number of defective bulbs in each of \(200\) boxes. <table> <tr><th>Number of defective bulbs</th><th>0</th><th>1</th><th>2</th><th>3 or more</th></tr> <tr><td>Number of boxes</td><td>164</td><td>22</td><td>10</td><td>4</td></tr> </table> Find the relative frequency for each category. Give each result as a decimal and a percent.

Two archers, Ethan and Maya, each completed several sets of \(5\) shots. The table shows how many bullseyes they made in each set. <table> <tr><th>Bullseyes per set</th><th>0</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th></tr> <tr><td>Ethan (number of sets)</td><td>2</td><td>4</td><td>6</td><td>12</td><td>10</td><td>6</td></tr> <tr><td>Maya (number of sets)</td><td>1</td><td>2</td><td>5</td><td>7</td><td>15</td><td>10</td></tr> </table> a) Find the relative frequency of the event “at least \(4\) bullseyes” for each archer. b) Compare the results. Which archer has the greater relative frequency for this event?

A survey asked \(250\) households how many pets they own. - The relative frequency for “no pets” is \(0.36\). - Exactly \(90\) households have one pet. a) How many surveyed households have no pets? b) Find the relative frequency of households with exactly one pet. c) All remaining households have either \(2\) or \(3\) pets. What must the sum of the relative frequencies of those two categories be? Briefly explain.

A class surveyed students about their favorite fruit. Each student chose exactly one fruit. The bar graph shows the results. Find the relative frequency of each fruit as a percent.

A sixth-grade class surveyed students about their favorite sports. The bar graph shows the results. a) How many students participated in the survey? b) Find the relative frequency for soccer as a fraction in simplest form and as a percent.

A survey of \(75\) students has this relative-frequency distribution: - Option P: \(0.48\) - Option Q: \(0.24\) - Option R: \(0.28\) Find the count for each option. Then determine whether Option P was selected exactly twice as often as Option Q.

A report says, “\(36\) of \(45\) completed tasks were checked, so the relative frequency is \(\frac{45}{36}=1.25=125\%\).” Identify the error, give the correct relative frequency as a fraction, decimal, and percent, and explain why the reported percent is impossible in this context.

At Exhibit A, \(7\) of \(20\) visitors completed a challenge. At Exhibit B, \(9\) of \(25\) visitors completed it. Find each relative frequency as a decimal and percent. Which exhibit has the higher completion rate, and by how many percentage points?

A wildlife camera recorded \(9\) bird images, \(6\) deer images, \(5\) raccoon images, and \(4\) empty images. a) What is the relative frequency that an image contains an animal? b) What is the relative frequency that an image contains a mammal? Give each answer as a fraction and a percent rounded to the nearest tenth of a percent.

Of \(72\) weather observations, \(27\) were sunny and \(18\) were cloudy. The rest were rainy. Find the count and relative frequency for each category. Give each relative frequency as a simplified fraction and decimal.

A team’s goals per game were summarized as follows. <table><tr><th>Goals</th><th>Number of games</th></tr><tr><td>\(0\)</td><td>\(8\)</td></tr><tr><td>\(1\)</td><td>\(12\)</td></tr><tr><td>\(2\)</td><td>\(6\)</td></tr><tr><td>\(3\)</td><td>\(4\)</td></tr></table> Find the relative frequency of games with at least \(2\) goals and the relative frequency of games with fewer than \(2\) goals. Give fractions and percents.

A robot completed \(90\) route tests: \(27\) on Route A, \(36\) on Route B, \(18\) on Route C, and \(9\) on Route D. Find each route’s relative frequency. Then find the combined relative frequency for Routes A and C.

Two reading groups each had a \(25\%\) relative frequency of students choosing an audiobook. Group A had \(48\) students, and Group B had \(84\) students. Find the count in each group and the difference between the counts. Explain why equal relative frequencies do not give equal counts.

A dot plot contains \(15\) observations. Exactly \(40\%\) of the dots are at \(6\), exactly \(\frac{1}{3}\) are at \(7\), and all remaining dots are at \(8\). Find the three stack heights and identify the mode.

Of \(250\) inspected devices, \(197\) passed immediately, \(38\) passed after a recheck, and \(15\) did not pass. Find the relative frequency of passing immediately, passing eventually, and not passing.

In a class survey, \(6\) of \(24\) students chose basketball as their favorite sport. What was basketball's relative frequency, as a fraction? How many degrees should its slice have in a circle graph of the survey?

Two classes answered a favorite-color survey: <table><tr><th></th><th>Red</th><th>Blue</th><th>Total</th></tr><tr><td>Class A</td><td>3</td><td>9</td><td>12</td></tr><tr><td>Class B</td><td>5</td><td>3</td><td>8</td></tr></table> What percent of each class chose red? Which class had the greater red share?

Give the relative frequency, as a percent, for \(1\), \(2\), and \(3\) pets in the dot plot.

A park surveyed hikers about their favorite trail. Creek received \(12\) votes, Hill received \(8\), and Woods received \(10\). A sign says, “More than half of the hikers chose Creek.” Is that true? Find Creek's relative frequency to explain.

Students voted for a fruit for snack time. The results were: <table><tr><th>Fruit</th><th>Students</th></tr><tr><td>Apple</td><td>9</td></tr><tr><td>Banana</td><td>12</td></tr><tr><td>Orange</td><td>9</td></tr></table> A student says, “The relative frequency for Apple is \(9\).” Explain the mistake and find the correct relative frequency.

Forty students chose their favorite after-school club. a) What fraction of the students chose Chess? Show how you found it from the angle. b) How many students chose Chess?

Volunteers counted butterflies at a nature center. They saw \(9\) monarch butterflies, which were \(\frac{1}{4}\) of all the butterflies they counted. a) How many butterflies did the volunteers count altogether? b) How many were not monarch butterflies?

Two sixth-grade classes were surveyed about their favorite type of pet. The results are summarized in the table. <table> <thead><tr><th>Class</th><th>Dog</th><th>Cat</th><th>Other</th><th>Total</th></tr></thead> <tbody> <tr><td>6A</td><td>8</td><td>6</td><td>6</td><td>20</td></tr> <tr><td>6B</td><td>10</td><td>5</td><td>10</td><td>25</td></tr> </tbody> </table> a) Find the relative frequency of each response category as a percent for both classes. b) In which class was the relative frequency of students who chose cats greater? Briefly justify your answer using your results from part a).

A bicycle shop has \(50\) bicycles in stock. The owner started the table below but left some entries blank. <table> <thead><tr><th>Bicycle type</th><th>Count</th><th>Relative frequency (percent)</th></tr></thead> <tbody> <tr><td>Mountain bike</td><td>20</td><td>?</td></tr> <tr><td>City bike</td><td>15</td><td>?</td></tr> <tr><td>Electric bike</td><td>?</td><td>?</td></tr> </tbody> </table> a) Find the missing number of electric bikes. b) Complete the relative-frequency column by finding the percent for each bicycle type. c) Check that your percentages add to \(100\%\).

Two sixth-grade classes participated in a donation drive. - In Class 6A, \(12\) of \(20\) students donated. - In Class 6B, \(15\) of \(30\) students donated. The Class 6B representative says, “Our class participated more because more students donated in our class than in Class 6A.” Use relative frequencies as percentages to evaluate the claim. Which class had the greater participation rate? Show your calculations.

A survey asked \(150\) sixth-grade students to choose their favorite school subject. The results were: - Math: \(45\) - Science: \(30\) - English language arts: \(15\) - Physical education: \(60\) a) Find the relative frequency of each subject as a percent. b) Find the corresponding central angle for each category in a circle graph. c) Kagiso says, “More than one third of the students chose physical education.” Is Kagiso correct? Justify your answer using part a).

Two classes compare how often students borrow books from the library. In Class 6A, \(15\) of \(25\) students regularly borrow books. In Class 6B, \(18\) of \(30\) students regularly borrow books. a) Find the relative frequency of regular library users in each class as a percent. b) Which class has the greater relative frequency? c) Suppose you display the results in a bar graph. Explain why percentages provide a fairer comparison than the numbers of students.

A survey asked \(40\) eighth-grade students how they travel to school. <table><tr><th>Travel method</th><th>Bike</th><th>Bus</th><th>Walk</th><th>Car</th></tr><tr><td>Students</td><td>10</td><td>16</td><td>10</td><td>4</td></tr></table> a) Find the relative frequency of each method as a percent. b) What fraction and percent of those surveyed do not travel by car? c) A circle graph will show the results. What central angle should the bus sector have?

All \(120\) eighth-grade students at a school choose one elective course. - \(30\%\) choose French. - \(45\) choose engineering and technology. - The rest choose computer science. a) How many choose French? b) Find the relative frequency of engineering and technology. c) Find the relative frequency of computer science.

A class made a circle graph of its math test grades. The sectors have these central angles: - A: \(30^\circ\) - B: \(120^\circ\) - C: \(90^\circ\) - D: \(60^\circ\) - F: \(60^\circ\) a) What percent of tests earned a C? b) What fraction of tests earned an A or B? Give the percent to the nearest tenth. c) Exactly \(4\) students earned a D. How many students took the test?

A recreation program surveyed all \(80\) students about their favorite sport. Some results are shown as percentages. <table> <tr><td><b>Sport</b></td><td><b>Share (percent)</b></td><td><b>Number of students</b></td></tr> <tr><td>Soccer</td><td>\(25\%\)</td><td>?</td></tr> <tr><td>Basketball</td><td>\(20\%\)</td><td>?</td></tr> <tr><td>Tennis</td><td>?</td><td>\(8\)</td></tr> <tr><td>Other</td><td>?</td><td>?</td></tr> </table> a) Complete the table by finding the missing counts and percentages. b) In a bar graph with the sports on the x-axis, which category would have the tallest bar?

A sixth-grade class completed a survey about how students travel to school. The bar graph shows the results. a) How many students participated in the survey? b) Find the relative frequency of each transportation method as a percent. c) Which transportation method is used by the most students?

Visitors to a community youth center were surveyed about their favorite hobby. Each person chose exactly one response. The bar graph shows the results. a) Find the frequency, or count, for “favorite hobby is sports or reading.” b) Find the relative frequency for gaming as a fraction in simplest form and as a percent.

A survey asked \(40\) students to choose their preferred recess snack. The bar graph shows the relative frequencies. Which distribution in the table matches the graph exactly? Justify the match by checking enough categories to rule out both other rows. <table><tr><th>Distribution</th><th>Apple</th><th>Pretzel</th><th>Snack bar</th><th>Yogurt</th></tr><tr><td>Distribution 1</td><td>\(10\)</td><td>\(16\)</td><td>\(8\)</td><td>\(6\)</td></tr><tr><td>Distribution 2</td><td>\(10\)</td><td>\(14\)</td><td>\(10\)</td><td>\(6\)</td></tr><tr><td>Distribution 3</td><td>\(8\)</td><td>\(16\)</td><td>\(8\)</td><td>\(8\)</td></tr></table>

A survey asked \(40\) sixth-grade students to choose their favorite hobby. The bar graph shows the results. Which statements are true? 1) More than one third of the students chose Sports. 2) Music and Reading together were more popular than Sports. 3) Gaming represents exactly \(25\%\) of all responses. 4) More than half of the class chose either Sports or Reading.

In Group A, \(80\%\) of \(10\) people solve a problem. In Group B, \(40\%\) of \(30\) people solve it. Mia averages the two percentages and gets \(60\%\). Is \(60\%\) the percent of all people who solved the problem?

On the first day of a museum program, \(12\) of \(30\) visitors chose the rooftop tour. On the second day, an unknown number of the \(20\) visitors chose it. Across both days, the relative frequency of choosing the rooftop tour was \(0.40\). How many second-day visitors chose the rooftop tour?

A field camera recorded the surface under \(80\) animal tracks. The relative frequency for sand was \(0.275\), and the relative frequency for mud was \(0.35\). Every track was classified as sand, mud, or gravel. Find the count and relative frequency for each surface.

A mural contains \(80\) tiles. The relative frequency of warm-color tiles is \(0.45\), the relative frequency of cool-color tiles is \(0.325\), and all remaining tiles are neutral. Among the neutral tiles, \(10\) are gray and the rest are white. Find the count and relative frequency for warm, cool, gray, and white tiles.

A survey received \(72\) forms. Six forms were blank. Of the completed forms, \(22\) selected “evening session.” a) Find the relative frequency of “evening session” among all returned forms. b) Find its relative frequency among completed forms only. c) Explain why the two relative frequencies differ.

In a vote with \(37\) valid ballots, Candidate A received \(13\) votes, Candidate B received \(12\), and Candidate C received \(12\). a) Find each candidate’s relative frequency as a percent to the nearest tenth. b) Round each percent to the nearest whole percent and add the rounded values. c) Explain why the rounded total is not exactly \(100\%\).

In a collection survey, \(9\) responses represent a relative frequency of \(0.375\). a) How many responses were collected in all? b) A different category received \(5\) responses. Find its relative frequency as a fraction, as a decimal to the nearest thousandth, and as a percent to the nearest tenth.

In the first \(30\) responses to a survey, \(18\) people selected Option A. Ten more responses arrived, and \(4\) of those selected Option A. Find the relative frequency of Option A before and after the new responses. Did the count and the relative frequency change in the same direction? Explain.

A survey of \(40\) visitors produced this table. One relative frequency is incorrect. <table> <tr><th>Choice</th><th>Count</th><th>Reported relative frequency</th></tr> <tr><td>A</td><td>\(12\)</td><td>\(0.30\)</td></tr> <tr><td>B</td><td>\(10\)</td><td>\(0.25\)</td></tr> <tr><td>C</td><td>\(8\)</td><td>\(0.20\)</td></tr> <tr><td>D</td><td>\(10\)</td><td>\(0.20\)</td></tr> </table> Identify and correct the error. Give two different checks that confirm your correction.

An archive initially has \(64\) labeled photographs, and \(8\) show a lighthouse. Later, \(64\) more photographs are added, but none show a lighthouse. Find the lighthouse relative frequency before and after the addition. Explain why the count stays the same while the relative frequency changes.

Fifty students could select every workshop that interested them. Music was selected by \(28\) students, sports by \(32\), and coding by \(20\). Find the relative frequency of each selection. Add the three relative frequencies and explain why the total can be greater than \(1\).

A collection has \(40\) labeled objects: \(18\) in category A, \(12\) in category B, and \(10\) in category C. Two objects are reclassified from B to C. a) Find the relative frequencies of A, B, and C before and after the change. b) Explain why the combined relative frequency of B and C does not change.

A category contains \(14\) observations and has relative frequency \(\frac{7}{15}\). a) How many observations are in the full data set? b) Six new observations are added, and none belong to the category. Find the new relative frequency as a fraction, as a decimal to the nearest thousandth, and as a percent to the nearest tenth.

Two equal-size groups of \(40\) students answered the same question. In Group A, the selected category had relative frequency \(0.35\). In Group B, it had relative frequency \(0.55\). Find the category count in each group and its relative frequency in the combined group of \(80\) students. Explain why the combined relative frequency is the average of the two group frequencies in this case.

In a survey, \(25\%\) of students chose blue, and \(15\%\) chose yellow. The remaining students chose red or green. The relative frequency for red was twice the relative frequency for green. Find the relative frequency of every color. If \(80\) students were surveyed, find each color's count.

The histogram shows how long students spent on an art activity. Convert its bar heights to relative frequencies. What stays the same, and what changes, if it is redrawn as a relative-frequency histogram?

In a school survey, \(12\) of the \(80\) students were left-handed. Of those \(12\) students, \(5\) chose blue as their favorite color. Find the relative frequency of choosing blue among the left-handed students and the relative frequency of being both left-handed and choosing blue among all surveyed students. Explain why the denominators differ.

During the first \(30\) shuttle arrivals, the relative frequency of arriving on time was \(0.70\). During the next \(20\) arrivals, \(14\) were on time. Find the combined relative frequency of on-time arrivals. Explain why it is unchanged.

A histogram summarizes \(40\) observations. The middle interval contains \(35\%\) of all observations. The two outermost intervals have frequencies \(6\) and \(4\). Find the frequency of the middle interval. Then find the combined relative frequency of the two outermost intervals.

A scanner report included \(120\) items, and \(18\) were marked for review. Later, workers learned that \(20\) test items had been included by mistake; \(8\) of those test items were marked for review. Find the original relative frequency marked for review and the corrected relative frequency after removing all test items.

In a survey with three exclusive choices, Choice A had relative frequency \(0.45\), Choice B had relative frequency \(0.35\), and \(8\) people chose Choice C. Find the total number surveyed and the counts for Choices A and B.

A relative-frequency histogram shows how many minutes students practiced a song. What would the interval counts be for a group of \(10\) students? What would they be for a group of \(20\)? Why can't the group size be found from this histogram alone?

Histograms A and B show students' reading times in minutes. Which group has the greater share of students who read for \(10\) to less than \(20\) minutes? Give both shares.

A report says an outcome had relative frequency \(0.33\) in \(30\) trials. Could \(0.33\) be the exact relative frequency? If it was rounded to the nearest hundredth, what whole-number count produced it? State the unrounded fraction.

Three exclusive categories have relative frequencies \(\frac{1}{4}\), \(\frac{3}{10}\), and \(\frac{9}{20}\). What is the smallest possible whole-number total of observations? Find the corresponding count in each category and explain why no smaller total works.