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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":"19d4d592-0720-b62f-8675-547a85f8f4bd","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":"4feb81dc-c77f-c0f0-fd7f-dee4aaee2559","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":"1f1a2e33-1be1-d25f-dace-e74cf506d016","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":"0c9b06b8-0aa5-a77f-3a2f-cc37b9b0653d","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":"bb7d8ea5-ee84-a261-eb29-ec503615f905","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":"d43428b6-3abd-f766-2681-3cff939aaa93","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":"f8687f0f-d705-fd42-5821-6cb782001618","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":"4365627d-3a80-31c1-c8fe-ad00ae4be66e","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":"b40ef6ac-f6d9-fa66-5f1c-98f635d6e162","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":"7dbce757-c349-4d00-80d1-5e27f850c68e","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":"83386668-1134-1946-7edd-78eebe095c69","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":"5e18643e-1631-235c-495e-075d5c0394d2","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":"b046b9fb-608e-354c-6234-13201da701bf","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":"e14d7560-c769-1a4b-cf01-a48c700fcc01","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":"c8862b82-ddbb-6205-6cd6-bded452bcb21","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":"a0b05bff-8d14-45e5-e0e1-60b375f7aca7","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":"723385cd-236c-4241-49af-e0f0b03f55ca","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":"8a6aad77-ecb5-16ef-7607-1ba4a2d39c12","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":"c0582cac-f7c5-961d-4c2e-b7cf27736791","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":"0e93ed7a-7d6e-9b94-3bdc-08618dbdd15f","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":"d236301f-0887-3d84-d72b-f81dc8efc9f2","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":"6c3c7212-0fb5-625a-9b66-dac76adc4209","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":{"examDate":"2027-05-14","paperLabel":"Component 1"},"heading":"Frequency Trees","title":"Frequency Trees Flashcards","topbar":{"backHref":"/gcse/maths/eduqas/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"d6bb6308-8110-42b1-93d8-c16708070960","walled":"$L39"}],"$L3a","$L3b"]