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Each number shown at a node is therefore a count, rather than a fraction or percentage."},{"text":"The percentage of items or people in a category.","correct":false,"explanation":"A percentage describes a proportion out of 100, not the frequency itself. The frequency is the count of items or people belonging to the category."},{"text":"The probability of items or people being in a category.","correct":false,"explanation":"Probability measures how likely an outcome is, whereas a frequency tree displays actual counts. The frequency is the count of items or people in the category."},{"text":"The difference between the numbers in two categories.","correct":false,"explanation":"Comparing two category totals may produce a difference, but that is not a frequency. A frequency is the count of items or people within one category."}]},{"id":"8dd032a1-afc8-081b-5ccd-acde34e3a146","cardType":"basic","points":1,"front":"How is a missing child node calculated if the parent total and one child are known?","back":"Subtract the known child from the parent total.","mcqOptions":[{"text":"Subtract the known child from the parent total.","correct":true,"explanation":"The two child frequencies must add to the parent total. Removing the known child frequency from that total leaves the frequency of the missing child node."},{"text":"Add the known child to the parent total.","correct":false,"explanation":"Adding the known child counts it again and produces a value larger than the remaining group. Subtract the known child from the parent total to find the missing child."},{"text":"Divide the parent total by the known child.","correct":false,"explanation":"Division finds a ratio, not the remaining frequency. Since the child nodes combine to make the parent total, subtract the known child from the parent total."},{"text":"Multiply the known child by the parent total.","correct":false,"explanation":"Multiplication does not separate the parent total into its two child groups and gives an unrealistically large result. The missing child is found using subtraction."}]},{"id":"9e30bf96-7a70-2e9a-7167-b3c122d7cb95","cardType":"basic","points":1,"front":"In a frequency tree, what does a branch represent?","back":"A category or choice that splits a total into groups.","mcqOptions":[{"text":"A category or choice that splits a total into groups.","correct":true,"explanation":"Each branch labels or represents one possible category or choice. Following the branches shows how the frequency at a parent node is separated into smaller groups."},{"text":"A total that combines all previous groups into one.","correct":false,"explanation":"A total is written at a node, whereas a branch shows how that total is divided. It represents a category or choice that splits the total into groups."},{"text":"A frequency showing the number in the whole sample.","correct":false,"explanation":"A frequency is a numerical count displayed at a node, not the connecting branch. A branch represents a category or choice used to split a total."},{"text":"A calculation that changes a frequency into a percentage.","correct":false,"explanation":"Frequency-tree branches organise counts rather than convert them into percentages. A branch represents a category or choice that divides a total into separate groups."}]},{"id":"4aa50acf-8bdf-298c-fb7d-089d167eccc3","cardType":"cloze","points":null,"front":"In a frequency tree, the [ ] must equal the sum of its connected child nodes.","back":"In a frequency tree, the parent node must equal the sum of its connected child nodes.","mcqOptions":[{"text":"parent node","correct":true,"explanation":"A parent node gives the total before the next split. Its connected child nodes divide that total into categories, so their frequencies must add back to the parent."},{"text":"child node","correct":false,"explanation":"A child node is only one of the smaller groups and does not normally equal the sum of its siblings. The parent node equals the sum of its connected child nodes."},{"text":"branch label","correct":false,"explanation":"A branch label names a category and is not a numerical total that can equal a sum. The parent node must equal the sum of its connected child nodes."},{"text":"final category","correct":false,"explanation":"A final category is one part of the split, not the combined total of the connected groups. The parent node is the value equal to the children’s sum."}]},{"id":"fb06df62-7f6c-02fb-c63e-3ac193faed1d","cardType":"cloze","points":null,"front":"In a frequency tree, the parent node must equal the sum of its connected [ ].","back":"In a frequency tree, the parent node must equal the sum of its connected child nodes.","mcqOptions":[{"text":"child nodes","correct":true,"explanation":"Child nodes show the frequencies after a parent total has been split into categories. Adding all connected child-node frequencies must reproduce the value at the parent node."},{"text":"parent nodes","correct":false,"explanation":"Parent nodes contain the totals being split, so they are not the smaller connected values being added. A parent node equals the sum of its connected child nodes."},{"text":"branch labels","correct":false,"explanation":"Branch labels name the categories and are not numerical frequencies that can be added. The values summed to reproduce the parent total are those at the connected child nodes."},{"text":"starting totals","correct":false,"explanation":"Starting totals occur earlier in the tree and are not the groups directly produced by a split. The parent node equals the sum of its connected child nodes."}]},{"id":"bfb22101-c62b-e365-cee7-850167da09d3","cardType":"basic","points":1,"front":"If 62 people are surveyed and 27 are boys, how many are girls?","back":"35 (62 - 27 = 35).","mcqOptions":[{"text":"35 (62 - 27 = 35).","correct":true,"explanation":"The boys and girls together make the total of 62 people. Subtracting the 27 boys leaves 35 people, so 35 of those surveyed are girls."},{"text":"89 (62 + 27 = 89).","correct":false,"explanation":"Adding gives the combined value of 62 and 27 rather than the number remaining within the surveyed total. Subtracting the 27 boys from 62 gives 35 girls."},{"text":"34 (62 - 27 = 34).","correct":false,"explanation":"This is an off-by-one subtraction error. Correctly subtracting 27 from 62 gives 35, so there are 35 girls in the surveyed group."},{"text":"45 (62 - 27 = 45).","correct":false,"explanation":"This results from an incorrect subtraction in the units and tens columns. Borrowing correctly gives 12 - 7 = 5 and 5 - 2 = 3, making 35."}]},{"id":"91ef067e-03e8-e7a7-b7d2-6d9595114c0d","cardType":"cloze","points":null,"front":"Frequency trees are generally read from [ ] to right.","back":"Frequency trees are generally read from left to right.","mcqOptions":[{"text":"left","correct":true,"explanation":"The initial total is generally placed on the left, with branches extending towards later categories on the right. The tree is therefore read from left to right."},{"text":"right","correct":false,"explanation":"Starting on the right would reverse the usual structure and make the sentence imply no movement across the tree. Frequency trees are generally read from left to right."},{"text":"top","correct":false,"explanation":"Some diagrams can be arranged vertically, but the stated standard orientation is horizontal. Frequency trees are generally followed from the starting total on the left towards the right."},{"text":"bottom","correct":false,"explanation":"Bottom-to-right does not describe the usual direction of a frequency tree. The starting total is generally on the left, so the diagram is read from left to right."}]},{"id":"a07b4fde-b67a-932c-dc76-82ba8e5e9a8f","cardType":"cloze","points":null,"front":"Frequency trees are generally read from left to [ ].","back":"Frequency trees are generally read from left to right.","mcqOptions":[{"text":"right","correct":true,"explanation":"Branches generally extend from an initial total on the left towards increasingly specific groups on the right. Following this structure means reading the frequency tree from left to right."},{"text":"left","correct":false,"explanation":"Reading from left to left would not move through the branches towards the later groups. Frequency trees usually begin with the total on the left and continue to the right."},{"text":"top","correct":false,"explanation":"The top may contain one category, but it is not the general reading direction stated here. Frequency trees are normally followed horizontally from left to right."},{"text":"bottom","correct":false,"explanation":"The lower branch represents one possible category rather than the overall reading direction. Frequency trees are generally read from the initial total on the left to the right."}]},{"id":"1a6cba82-c95d-6774-30e0-e159ad75e0d5","cardType":"basic","points":2,"front":"Where should an overall total (e.g. \"52 students chose drink A\") be placed in a tree split by Gender then Drink?","back":"It is the sum of both \"Drink A\" nodes (not a single node).","mcqOptions":[{"text":"It is the sum of both \"Drink A\" nodes (not a single node).","correct":true,"explanation":"Because the tree first separates students by gender, Drink A appears once under each gender. The overall Drink A total is found by adding those two frequencies."},{"text":"It is the sum of both \"Drink B\" nodes (not a single node).","correct":false,"explanation":"This selects the branches for the wrong drink. The overall Drink A total is the sum of the two Drink A nodes, one under each gender."},{"text":"It is placed in the first \"Drink A\" node (not split between nodes).","correct":false,"explanation":"This treats one gender branch as though it represents everyone. The total must be split between genders, so the two Drink A nodes must sum to 52."},{"text":"It is the difference between both \"Drink A\" nodes (not their sum).","correct":false,"explanation":"Subtracting would compare the Drink A frequencies for the two genders rather than combine them. The overall total is found by adding both Drink A nodes."}]},{"id":"fa7f59bd-a510-41b6-5a1f-5b806cb5f701","cardType":"cloze","points":null,"front":"To calculate a frequency from a fraction clue, use the formula: $$part = \\text{group total} \\times \\text{[...]}$$","back":"To calculate a frequency from a fraction clue, use the formula: $$part = \\text{group total} \\times \\boxed{fraction}$$","mcqOptions":[{"text":"fraction","correct":true,"explanation":"A fractional part of a group is calculated by multiplying the group total by the given fraction, such as $40 \\times \\frac{3}{5}$."},{"text":"denominator","correct":false,"explanation":"Using only the denominator ignores the numerator and therefore the required number of equal parts. Multiply the group total by the complete fraction."},{"text":"numerator","correct":false,"explanation":"Multiplying by only the numerator omits the division represented by the denominator. The correct multiplier is the complete fraction given in the clue."},{"text":"reciprocal","correct":false,"explanation":"Using the reciprocal reverses the fraction and usually produces an excessive value. The group total must be multiplied by the original fraction, not its reciprocal."}]},{"id":"b2dae4dd-89a5-02c7-4fad-28b88180a9c6","cardType":"basic","points":1,"front":"When given a clue like \"$\\frac{2}{5}$ of the girls\", which frequency is used as the total for the calculation?","back":"The girls total.","mcqOptions":[{"text":"The girls total.","correct":true,"explanation":"The phrase “of the girls” names the whole group to which the fraction applies, so the girls total must be multiplied by $\\frac{2}{5}$."},{"text":"The boys total.","correct":false,"explanation":"This uses the other gender’s frequency rather than the group named in the clue. The words “of the girls” mean the girls total is required."},{"text":"The students total.","correct":false,"explanation":"This incorrectly applies the fraction to everyone in the tree. Since the clue specifies “of the girls”, the calculation must use only the girls total."},{"text":"The selected branch total.","correct":false,"explanation":"This confuses the unknown part with the starting total. The named group is the girls, so their total is used before finding the required branch frequency."}]},{"id":"b78a274a-3ca8-bb4c-2d73-c7b7b8b18120","cardType":"basic","points":1,"front":"If 40 students play tennis and $\\frac{3}{5}$ go on Saturday, how many go on Saturday?","back":"24 students ($$40 \\times \\frac{3}{5} = 24$$).","mcqOptions":[{"text":"24 students ($$40 \\times \\frac{3}{5} = 24$$).","correct":true,"explanation":"Dividing 40 into five equal parts gives 8 students per fifth, and taking three of those parts gives $3 \\times 8 = 24$ students."},{"text":"8 students ($$40 \\div 5 = 8$$).","correct":false,"explanation":"This finds one fifth of the students but forgets to take three fifths. Multiplying 8 by the numerator 3 gives the correct answer of 24 students."},{"text":"16 students ($$40 \\times \\frac{2}{5} = 16$$).","correct":false,"explanation":"This calculates the complementary fraction $\\frac{2}{5}$ who do not go on Saturday. The required $\\frac{3}{5}$ of 40 is 24 students."},{"text":"120 students ($$40 \\times 3 = 120$$).","correct":false,"explanation":"This multiplies by the numerator but ignores division by the denominator. The calculation must use the whole fraction: $40 \\times \\frac{3}{5} = 24$."}]},{"id":"f400a098-f5b1-60e8-c241-3880dcbc1316","cardType":"cloze","points":null,"front":"In a fraction clue, the words [ ] identify which group total to use.","back":"In a fraction clue, the words \"of the\" identify which group total to use.","mcqOptions":[{"text":"\"of the\"","correct":true,"explanation":"The words “of the” introduce the group that acts as the whole in a fraction calculation, so the total immediately following them is used."},{"text":"\"out of\"","correct":false,"explanation":"The words “out of” usually describe a ratio between a favourable number and a total. In a fraction clue, “of the” identifies the group total to multiply."},{"text":"\"more than\"","correct":false,"explanation":"The words “more than” describe an increase or comparison, not the whole group for a fractional calculation. The group total is identified by “of the”."},{"text":"\"fewer than\"","correct":false,"explanation":"The words “fewer than” indicate a comparison or subtraction rather than a fractional part of a group. The relevant total follows the words “of the”."}]},{"id":"398bcac6-b305-e245-7371-06f8f8d09f2b","cardType":"basic","points":1,"front":"How do you determine the denominator for a probability question from a tree?","back":"It is the frequency of the group being chosen from.","mcqOptions":[{"text":"It is the frequency of the group being chosen from.","correct":true,"explanation":"The denominator counts all possible people or items available for selection. Therefore, it is the total frequency of the group from which the choice is made."},{"text":"It is the frequency of the outcome being asked for.","correct":false,"explanation":"This confuses the numerator with the denominator. The desired outcome supplies the numerator, while the total group being chosen from supplies the denominator."},{"text":"It is the frequency of the largest branch in the tree.","correct":false,"explanation":"Branch size does not determine a probability denominator. The denominator must count every possible selection within the group specified in the question."},{"text":"It is the frequency of the whole sample in every question.","correct":false,"explanation":"Using the whole sample ignores conditional wording that restricts the choice to a subgroup. The denominator is the frequency of the group actually being chosen from."}]},{"id":"9d47ca93-96f8-06e1-15d6-78dcafd39fb3","cardType":"basic","points":1,"front":"If the question says \"One of the left-handed people is chosen\", what is the denominator?","back":"The total frequency of left-handed people.","mcqOptions":[{"text":"The total frequency of left-handed people.","correct":true,"explanation":"The choice is restricted to left-handed people, so every left-handed person is a possible selection. Their total frequency therefore forms the denominator."},{"text":"The total frequency of all people.","correct":false,"explanation":"This ignores the restriction to left-handed people and makes the sample space too large. The denominator is only the total frequency of left-handed people."},{"text":"The total frequency of right-handed people.","correct":false,"explanation":"This uses the opposite group from the one named in the question. Since the person is chosen from left-handed people, their total is the denominator."},{"text":"The wanted frequency of left-handed people.","correct":false,"explanation":"This confuses the favourable outcome with all possible choices. The wanted left-handed subgroup forms the numerator, while all left-handed people form the denominator."}]},{"id":"22e3cea2-5155-587f-e4e5-e45a78aeb3a3","cardType":"cloze","points":null,"front":"Probability from frequencies is calculated as: $$\\frac{\\text{[...]}}{\\text{number possible}}$$","back":"Probability from frequencies is calculated as: $$\\frac{\\boxed{\\text{number wanted}}}{\\text{number possible}}$$","mcqOptions":[{"text":"$$\\text{number wanted}$","correct":true,"explanation":"The numerator counts the outcomes that satisfy the condition being asked about, while the denominator counts all outcomes possible within the stated group."},{"text":"$$\\text{number possible}$","correct":false,"explanation":"Putting the number possible in both positions would incorrectly give a probability of 1. The numerator must be the number of outcomes wanted."},{"text":"$$\\text{group total}$","correct":false,"explanation":"The group total belongs in the denominator because it counts all possible selections. The numerator must count only those selections matching the required outcome."},{"text":"$$\\text{number unwanted}$","correct":false,"explanation":"This calculates the probability of the complementary outcome rather than the event requested. The numerator must be the number wanted, with the number possible below it."}]},{"id":"6d1a303a-ac35-e8e8-b4c6-e0fb59313984","cardType":"cloze","points":null,"front":"Probability from frequencies is calculated as: $$\\frac{\\text{number wanted}}{\\text{[...]}}$$","back":"Probability from frequencies is calculated as: $$\\frac{\\text{number wanted}}{\\boxed{\\text{number possible}}}$$","mcqOptions":[{"text":"$$\\text{number possible}$","correct":true,"explanation":"A probability from frequencies is the number of wanted outcomes divided by the total number of possible outcomes in the group from which the selection is made."},{"text":"$$\\text{number wanted}$","correct":false,"explanation":"Repeating the wanted frequency in the denominator would always produce a probability of 1. The denominator must be the number possible in the relevant group."},{"text":"$$\\text{number unwanted}$","correct":false,"explanation":"The unwanted frequency helps calculate the complementary probability, but it is not the denominator. Divide the number wanted by the total number possible."},{"text":"$$\\text{number remaining}$","correct":false,"explanation":"The number remaining is not necessarily the full sample space and may exclude wanted outcomes. The denominator must include every possible outcome in the relevant group."}]},{"id":"bb97fb00-04c5-eac3-fc14-9a0fdb716593","cardType":"basic","points":1,"front":"A tree shows 12 female left-handers out of 30 left-handers. What is the probability that a left-hander chosen at random is female?","back":"$$$\\frac{12}{30}$$ (or $\\frac{2}{5}$)","mcqOptions":[{"text":"$$$\\frac{12}{30}$$ (or $\\frac{2}{5}$)","correct":true,"explanation":"The selection is restricted to left-handers, so the denominator is all 30 left-handers. Of these, 12 are female, giving $\\frac{12}{30}=\\frac{2}{5}$."},{"text":"$$$\\frac{12}{70}$$ (or $\\frac{6}{35}$)","correct":false,"explanation":"Using 70 treats the selection as being made from all people. The person is chosen from the 30 left-handers, so the probability is $\\frac{12}{30}=\\frac{2}{5}$."},{"text":"$$$\\frac{30}{70}$$ (or $\\frac{3}{7}$)","correct":false,"explanation":"This calculates the proportion of all people who are left-handed, not the proportion of left-handers who are female. The required probability is $\\frac{12}{30}=\\frac{2}{5}$."},{"text":"$$$\\frac{18}{30}$$ (or $\\frac{3}{5}$)","correct":false,"explanation":"This uses the number of male left-handers, giving the complementary probability. Female left-handers account for 12 of the 30 left-handers, so the answer is $\\frac{12}{30}$."}]},{"id":"29ac1933-3021-661c-e58a-d880442e9acb","cardType":"basic","points":1,"front":"A tree shows 12 female left-handers out of 70 total people. What is the probability that a person chosen at random is a female left-hander?","back":"$$$\\frac{12}{70}$$ (or $\\frac{6}{35}$)","mcqOptions":[{"text":"$$$\\frac{12}{70}$$ (or $\\frac{6}{35}$)","correct":true,"explanation":"The person is chosen from all 70 people, so 70 is the denominator. There are 12 female left-handers, giving $\\frac{12}{70}=\\frac{6}{35}$."},{"text":"$$$\\frac{12}{30}$$ (or $\\frac{2}{5}$)","correct":false,"explanation":"Using 30 would be correct only if the person were chosen from the left-handers. Here the selection is from all 70 people, so the answer is $\\frac{12}{70}$."},{"text":"$$$\\frac{30}{70}$$ (or $\\frac{3}{7}$)","correct":false,"explanation":"This gives the probability that a randomly chosen person is left-handed, including both females and males. Only 12 are female left-handers, so the required probability is $\\frac{12}{70}$."},{"text":"$$$\\frac{58}{70}$$ (or $\\frac{29}{35}$)","correct":false,"explanation":"Subtracting 12 from 70 counts everyone who is not a female left-hander, producing the complementary probability. The required event has probability $\\frac{12}{70}=\\frac{6}{35}$."}]},{"id":"af488116-a6ce-9922-c4bc-14a6af2286b7","cardType":"basic","points":1,"front":"What is the exam technique for identifying the denominator for a probability question?","back":"Circle the group being chosen from on the tree.","mcqOptions":[{"text":"Circle the group being chosen from on the tree.","correct":true,"explanation":"The denominator is the total frequency of the group from which the selection is made. Circling that group helps distinguish it from the smaller group representing the wanted outcome."},{"text":"Circle the group matching the wanted outcome on the tree.","correct":false,"explanation":"The wanted outcome supplies the numerator rather than the denominator. To identify the denominator, circle the entire group from which the person or item is being chosen."},{"text":"Circle the final branch mentioned in the question.","correct":false,"explanation":"The final branch may identify the wanted outcome, but it does not necessarily represent every possible selection. Circle the group being chosen from to obtain the denominator."},{"text":"Circle the grand total at the start of the tree.","correct":false,"explanation":"The grand total is the denominator only when selection is from the entire population. For a conditional question, circle the particular group being chosen from instead."}]},{"id":"4bee8a8a-ff22-fd6c-7b1b-879e720bf1f9","cardType":"cloze","points":null,"front":"When a person is chosen from a particular group, the probability is called a [ ].","back":"When a person is chosen from a particular group, the probability is called a conditional probability.","mcqOptions":[{"text":"conditional probability","correct":true,"explanation":"A conditional probability measures the chance of an event when the possible outcomes have been restricted to a specified group or when another condition is already known."},{"text":"complementary probability","correct":false,"explanation":"A complementary probability is the chance that an event does not happen. Choosing from a specified group instead restricts the sample space, producing a conditional probability."},{"text":"experimental probability","correct":false,"explanation":"Experimental probability is estimated using observed results or frequencies. The key feature here is that selection is restricted to a particular group, making it a conditional probability."},{"text":"theoretical probability","correct":false,"explanation":"Theoretical probability is calculated from equally likely outcomes rather than observed data. Restricting the choice to a particular group describes a conditional probability."}]},{"id":"2e87dc6b-048d-c2cc-b7b1-892b73b844a5","cardType":"basic","points":1,"front":"What does the first node on the far left of a frequency tree typically contain?","back":"The grand total.","mcqOptions":[{"text":"The grand total.","correct":true,"explanation":"The far-left node represents the complete population before it is divided into categories. Its frequency is therefore the grand total for the whole tree."},{"text":"The first branch total.","correct":false,"explanation":"A first branch total appears after the initial split and represents only one category. The far-left node comes before any split and contains the grand total."},{"text":"The final category frequency.","correct":false,"explanation":"Final category frequencies appear at the ends of the tree after all divisions. The first node instead contains the grand total before categories are separated."},{"text":"The first outcome probability.","correct":false,"explanation":"A frequency tree records numbers of people or items rather than probabilities at its nodes. The far-left node typically shows the grand total for the population."}]},{"id":"7e22de9b-02da-beb5-3782-986d1306b078","cardType":"basic","points":2,"front":"How do you verify a frequency tree is completed correctly?","back":"

Ensure branches add up to their parent nodes
Ensure end nodes sum to the grand total

","mcqOptions":[{"text":"

Ensure branches add up to their parent nodes
Ensure end nodes sum to the grand total

","correct":true,"explanation":"Each parent frequency must be divided completely between its branches, so the child nodes add to the parent. All final categories must also account for the grand total."},{"text":"

Ensure branches multiply to their parent nodes
Ensure end nodes sum to the grand total

","correct":false,"explanation":"Multiplication is associated with some probability-tree calculations, not frequency-tree checks. Child branch frequencies must add to their parent, while all end nodes sum to the grand total."},{"text":"

Ensure branches add up to their parent nodes
Ensure end nodes equal the grand total

","correct":false,"explanation":"Individual end nodes represent separate final categories and should not each equal the whole population. They must collectively sum to the grand total, while branches add to parents."},{"text":"

Ensure branches subtract from their parent nodes
Ensure end nodes sum to the first branch

","correct":false,"explanation":"Subtraction can find a missing branch, but the completed child frequencies must add to their parent. All end nodes across the tree must sum to the grand total."}]}]}],"examCountdown":null,"heading":"Frequency Trees","title":"Frequency Trees Flashcards","topbar":{"backHref":"/gcse/maths/ccea/flashcards"},"topicSidebar":"$L39"}]}],"topicId":"deea27c1-e489-2b62-7b71-aab5f95e5837","walled":"$L3a"}],"$L3b","$L3c"]