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24:[["$","$L33",null,{"feature":"flashcards"}],"$L34",["$","$L35",null,{"href":"/igcse/maths/edexcel/grade-2-2-14-averages/flashcards","label":"Averages","subjectCode":"igcse_maths","surface":"flashcards"}],["$","$L36",null,{"runner":["$","div",null,{"className":"min-h-0 flex-1 overflow-hidden bg-background","children":["$","$L37",null,{"decks":[{"id":"a7a65df4-9f1d-4f18-b0a2-11826340f450","title":"Averages Flashcards","topicId":"9d76d594-4a4d-496b-a783-d6043f9c99ed","topicSlug":"grade-2-2-14-averages","cards":[{"id":"308dbcb0-6249-42cc-a9e0-7742c39cc933","cardType":"basic","points":1,"front":"What does the range describe about a set of data?","back":"How spread out the data values are.","mcqOptions":[{"text":"How spread out the data values are.","correct":true,"explanation":"The range measures the spread of the data by comparing its largest and smallest values. A larger range generally indicates that the values are more spread out."},{"text":"What the average of the data values is.","correct":false,"explanation":"This describes the mean, which indicates the central value obtained by sharing the total equally. The range instead describes how spread out the data values are."},{"text":"Which data value appears most often.","correct":false,"explanation":"This describes the mode, which identifies the value occurring most frequently. The range instead describes how spread out the data values are."},{"text":"Where the middle of the data values lies.","correct":false,"explanation":"This describes the median, which is the middle value after ordering the data. The range instead describes how spread out the data values are."}]},{"id":"dbcf1a42-9bd1-4b14-80d0-2c282f0ad696","cardType":"cloze","points":null,"front":"The formula for the range is: $\\text{range} = \\text{[...]} - \\text{smallest value}$.","back":"The formula for the range is: $\\text{range} = \\boxed{\\text{largest value}} - \\text{smallest value}$.","mcqOptions":[{"text":"$$\\text{largest value}$","correct":true,"explanation":"The range is calculated by subtracting the smallest value from the largest value, giving the distance between the two extremes of the data set."},{"text":"$$\\text{mean value}$","correct":false,"explanation":"Using the mean confuses a measure of central tendency with an extreme value. The correct first term is $\\text{largest value}$, from which the smallest value is subtracted."},{"text":"$$\\text{median value}$","correct":false,"explanation":"Using the median confuses the middle value with the upper extreme. The range is $\\text{largest value} - \\text{smallest value}$."},{"text":"$$\\text{smallest value}$","correct":false,"explanation":"Starting with the smallest value would mean subtracting it from itself, always producing zero. The correct first term is $\\text{largest value}$."}]},{"id":"21663ceb-6427-4785-9bf5-9eaf095581b2","cardType":"cloze","points":null,"front":"The formula for the range is: $\\text{range} = \\text{largest value} - \\text{[...]}$.","back":"The formula for the range is: $\\text{range} = \\text{largest value} - \\boxed{\\text{smallest value}}$.","mcqOptions":[{"text":"$$\\text{smallest value}$","correct":true,"explanation":"The range is the difference between the two extremes, so the smallest value is subtracted from the largest value."},{"text":"$$\\text{mean value}$","correct":false,"explanation":"Subtracting the mean confuses a measure of central tendency with the lower extreme. The range is found by subtracting the $\\text{smallest value}$ from the largest."},{"text":"$$\\text{median value}$","correct":false,"explanation":"Subtracting the median measures only part of the data’s spread. The range requires subtracting the $\\text{smallest value}$ from the largest value."},{"text":"$$\\text{largest value}$","correct":false,"explanation":"Subtracting the largest value from itself would always give zero. The required second term is the $\\text{smallest value}$."}]},{"id":"a3155a58-7cb8-4e9f-9be6-61595dbd7e6a","cardType":"cloze","points":null,"front":"When preparing a list of data for averages, ascending order means arranging values from [ ] to largest.","back":"When preparing a list of data for averages, ascending order means arranging values from smallest to largest.","mcqOptions":[{"text":"smallest","correct":true,"explanation":"Ascending order moves upwards in value, so the list begins with the smallest value and ends with the largest."},{"text":"largest","correct":false,"explanation":"Beginning with the largest value would produce descending order rather than ascending order. An ascending list runs from smallest to largest."},{"text":"mean","correct":false,"explanation":"The mean is a calculated average, not necessarily an endpoint of the ordered list. Ascending order starts with the smallest value."},{"text":"median","correct":false,"explanation":"The median is the middle value once the data is ordered, not the first value. Ascending order begins with the smallest value."}]},{"id":"7b356833-0655-4311-8ca1-9001ed9ec15d","cardType":"cloze","points":null,"front":"When preparing a list of data for averages, ascending order means arranging values from smallest to [ ].","back":"When preparing a list of data for averages, ascending order means arranging values from smallest to largest.","mcqOptions":[{"text":"largest","correct":true,"explanation":"Ascending order means values increase from left to right, so the sequence starts with the smallest value and finishes with the largest."},{"text":"smallest","correct":false,"explanation":"Ending with the smallest value reverses the required direction and describes descending order. An ascending list finishes with the largest value."},{"text":"mean","correct":false,"explanation":"The mean is calculated from all the data and is not necessarily the final ordered value. Ascending order ends with the largest value."},{"text":"median","correct":false,"explanation":"The median occupies the middle position in ordered data rather than the final position. Ascending order finishes with the largest value."}]},{"id":"025caeff-12a0-41a6-9331-363bcbfae7a5","cardType":"basic","points":1,"front":"How should repeated values be handled when putting a list in order?","back":"Write them every time they appear; they are essential for the mode, median, and mean.","mcqOptions":[{"text":"Write them every time they appear; they are essential for the mode, median, and mean.","correct":true,"explanation":"Each occurrence contributes to the frequency and total, and it can affect the middle position. Repeated values must therefore be retained when finding the mode, median, or mean."},{"text":"Write them only once in the list; duplicates do not affect any of the averages.","correct":false,"explanation":"Removing repeats changes frequencies, the number of values, and usually the total, producing unreliable averages. Write repeated values every time they appear."},{"text":"Write them at most twice in the list; further copies can always be ignored.","correct":false,"explanation":"Keeping only two copies arbitrarily changes the data whenever a value occurs more often. Every occurrence must be written because each one affects the averages."},{"text":"Write them only for the mode; they are irrelevant when calculating the median and mean.","correct":false,"explanation":"Repeated values affect more than the mode: they can change the median’s position and the mean’s total. Write them every time they appear."}]},{"id":"c864bd5e-3189-472f-9b32-a96befbd4b86","cardType":"cloze","points":null,"front":"The mode is the [ ] value in the data.","back":"The mode is the most frequent value in the data.","mcqOptions":[{"text":"most frequent","correct":true,"explanation":"The mode is determined by frequency: it is the value occurring more often than any other value in the data set."},{"text":"largest","correct":false,"explanation":"The largest value is simply the upper extreme and need not occur most often. The mode is the most frequent value."},{"text":"middle","correct":false,"explanation":"The middle value after ordering is the median, not the mode. The mode is identified as the most frequent value."},{"text":"least frequent","correct":false,"explanation":"The least frequent value is the opposite of what the mode identifies. The mode is the most frequent value in the data."}]},{"id":"78a20b49-4a3c-4b37-9313-dde27f381370","cardType":"basic","points":1,"front":"What is a common mistake when identifying the mode?","back":"Choosing the largest number instead of the one that appears most often.","mcqOptions":[{"text":"Choosing the largest number instead of the one that appears most often.","correct":true,"explanation":"The mode depends on frequency, not size. A common error is selecting the greatest value even when another value occurs more often."},{"text":"Choosing the middle number instead of the one that appears most often.","correct":false,"explanation":"This confuses the mode with the median, which is found from the middle of ordered data. The common mistake is choosing the largest number rather than the most frequent one."},{"text":"Choosing the calculated mean instead of the one that appears most often.","correct":false,"explanation":"This confuses the mode with the mean, which uses the total divided by the number of values. The relevant mistake is choosing the largest number instead of the most frequent one."},{"text":"Choosing the smallest number instead of the one that appears most often.","correct":false,"explanation":"The smallest number is another extreme, but the stated common misconception is assuming that mode means greatest. The mistake is choosing the largest number instead of the most frequent one."}]},{"id":"d12bd2a2-2d99-487b-bedd-acbe54a25368","cardType":"cloze","points":null,"front":"The median is the [ ] value when the data is arranged in order.","back":"The median is the middle value when the data is arranged in order.","mcqOptions":[{"text":"middle","correct":true,"explanation":"Once the values are arranged in order, the median is the middle value, separating the lower half of the data from the upper half."},{"text":"highest","correct":false,"explanation":"The highest value is the maximum, not the median. After arranging the data in order, the median is the middle value."},{"text":"lowest","correct":false,"explanation":"The lowest value is the minimum, not the median. The correct term is middle because the median lies at the centre of the ordered data."},{"text":"most frequent","correct":false,"explanation":"The most frequent value is the mode, not the median. The median is the middle value after all the data has been arranged in order."}]},{"id":"f50074f6-c478-4a23-a515-73deefd68914","cardType":"basic","points":1,"front":"What is the first step required to find the median?","back":"Put the numbers in ascending order.","mcqOptions":[{"text":"Put the numbers in ascending order.","correct":true,"explanation":"The median depends on position, so the values must first be arranged from smallest to largest. The middle value or values can then be identified."},{"text":"Add the numbers to find the total.","correct":false,"explanation":"Adding the numbers is part of calculating the mean, not the median. To find the median, first put the numbers in ascending order."},{"text":"Subtract the smallest number from the largest.","correct":false,"explanation":"Subtracting the smallest value from the largest calculates the range. To find the median, first arrange all the numbers in ascending order."},{"text":"Count how often each number occurs.","correct":false,"explanation":"Counting frequencies helps identify the mode, not the median. The first step for the median is to put the numbers in ascending order."}]},{"id":"c3c4ef43-30a7-43b5-8596-1e40ee59eb38","cardType":"basic","points":2,"front":"How do you find the median if there is an even number of values?","back":"

Identify the two middle values
Find their mean (add them and divide by 2)

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

Identify the two middle values
Find their mean (add them and divide by 2)

","correct":true,"explanation":"An even-sized ordered data set has two central values. Their mean gives the point halfway between them, which is the median of the data."},{"text":"

Identify the two middle values
Find their sum (add them without dividing)

","correct":false,"explanation":"Adding the two middle values without dividing makes the result twice as large as their mean. The median is their sum divided by 2."},{"text":"

Identify the two end values
Find their mean (add them and divide by 2)

","correct":false,"explanation":"Using the end values finds the midrange, not the median. For an even number of values, identify the two middle values and calculate their mean."},{"text":"

Identify the two middle values
Find their difference (subtract the smaller from the larger)

","correct":false,"explanation":"The difference measures the gap between the middle values, not their central value. The median is found by adding them and dividing by 2."}]},{"id":"6fd7af17-85bf-4bf9-b652-7fcd3617833f","cardType":"basic","points":2,"front":"A student says the median of 10, 2, 8 is 2 because it is in the middle. Why are they wrong?","back":"The list must be ordered first (2, 8, 10); the correct median is 8.","mcqOptions":[{"text":"The list must be ordered first (2, 8, 10); the correct median is 8.","correct":true,"explanation":"The median is based on position after ordering, not position in the original list. In the ordered list 2, 8, 10, the middle value is 8."},{"text":"The list does not need to be ordered; the correct median is 2.","correct":false,"explanation":"This treats the middle-written number as the median without sorting. The values must be ordered as 2, 8, 10, making the correct median 8."},{"text":"The list must be ordered first (2, 8, 10); the correct median is 10.","correct":false,"explanation":"Ordering the values is correct, but selecting 10 confuses the median with the maximum. The middle value of 2, 8, 10 is 8."},{"text":"The values must be added first (10 + 2 + 8); the correct median is 20.","correct":false,"explanation":"Adding all the values produces the total, which is used for the mean rather than the median. Ordering gives 2, 8, 10, so the median is 8."}]},{"id":"dbc175e6-a26e-488d-bfff-e202d179a605","cardType":"cloze","points":null,"front":"The mean is calculated as: $\\text{mean} = \\frac{\\text{[...]}}{\\text{number of values}}$.","back":"The mean is calculated as: $\\text{mean} = \\frac{\\boxed{\\text{total of values}}}{\\text{number of values}}$.","mcqOptions":[{"text":"$$\\text{total of values}$","correct":true,"explanation":"The mean shares the combined total equally among all the values, so its numerator is the total obtained by adding every value in the data set."},{"text":"$$\\text{number of values}$","correct":false,"explanation":"Using the count as both the numerator and denominator would always give 1. The numerator must be the total of values, divided by the number of values."},{"text":"$$\\text{largest value}$","correct":false,"explanation":"The largest value is the maximum and does not represent the combined data. The mean uses the total of all values as its numerator."},{"text":"$$\\text{range of values}$","correct":false,"explanation":"The range is the largest value minus the smallest and measures spread. The mean is calculated using the total of values as the numerator."}]},{"id":"c8621fd2-7a97-40e3-a510-7a0c49726e80","cardType":"cloze","points":null,"front":"The mean is calculated as: $\\text{mean} = \\frac{\\text{total of values}}{\\text{[...]}}$.","back":"The mean is calculated as: $\\text{mean} = \\frac{\\text{total of values}}{\\boxed{\\text{number of values}}}$.","mcqOptions":[{"text":"$$\\text{number of values}$","correct":true,"explanation":"Dividing the total by the number of values shares the total equally across every item, producing the arithmetic mean of the data."},{"text":"$$\\text{total of values}$","correct":false,"explanation":"Dividing the total by itself would normally give 1, not the mean. The denominator must be the number of values in the data set."},{"text":"$$\\text{number of gaps}$","correct":false,"explanation":"Counting gaps creates an off-by-one error because there is one fewer gap than values. The total must be divided by the number of values."},{"text":"$$\\text{range of values}$","correct":false,"explanation":"The range measures spread and is not the quantity used to share the total. The correct denominator is the number of values."}]},{"id":"94b8df3e-935d-4bbd-83d5-2a38b9bfb955","cardType":"basic","points":1,"front":"Conceptually, what does the mean represent regarding the data?","back":"The value each item would have if the total were shared out equally.","mcqOptions":[{"text":"The value each item would have if the total were shared out equally.","correct":true,"explanation":"The mean redistributes the total evenly while keeping that total unchanged. Each item would therefore have the mean if all values were shared equally."},{"text":"The value that appears with the greatest frequency.","correct":false,"explanation":"The value occurring most often is the mode, not the mean. The mean represents the equal share each item would receive from the total."},{"text":"The central value when the data is placed in order.","correct":false,"explanation":"The central ordered value is the median, not the mean. The mean is the value each item would have if the total were shared equally."},{"text":"The difference between the largest and smallest values.","correct":false,"explanation":"The difference between the extremes is the range, which measures spread. The mean represents an equal sharing of the total across all items."}]},{"id":"63562920-52f9-412d-9b68-6345d52ffc91","cardType":"cloze","points":null,"front":"To find the total when given the mean and the count: $\\text{total} = \\text{[...]} \\times \\text{number of values}$.","back":"To find the total when given the mean and the count: $\\text{total} = \\boxed{\\text{mean}} \\times \\text{number of values}$.","mcqOptions":[{"text":"$$\\text{mean}$","correct":true,"explanation":"The mean is the equal share for one value, so multiplying it by the number of values reconstructs the complete total."},{"text":"$$\\text{median}$","correct":false,"explanation":"The median describes the middle position and cannot generally reconstruct the total. The total is found by multiplying the mean by the number of values."},{"text":"$$\\text{mode}$","correct":false,"explanation":"The mode identifies the most frequent value and gives no reliable total. The required multiplier is the mean because it represents the equal share per value."},{"text":"$$\\text{range}$","correct":false,"explanation":"The range measures the spread between the largest and smallest values, not an equal share. Multiply the mean by the number of values to find the total."}]},{"id":"b8a7862a-f7c3-4663-8b58-ea05bd069e81","cardType":"cloze","points":null,"front":"To find the total when given the mean and the count: $\\text{total} = \\text{mean} \\times \\text{[...]}$.","back":"To find the total when given the mean and the count: $\\text{total} = \\text{mean} \\times \\boxed{\\text{number of values}}$.","mcqOptions":[{"text":"$$\\text{number of values}$","correct":true,"explanation":"The mean equals the total divided by the number of values, so reversing this relationship gives total equals mean multiplied by the number of values."},{"text":"$$\\text{sum of values}$","correct":false,"explanation":"The sum of the values is the total itself, so multiplying by it would not reverse the mean calculation. The mean must be multiplied by the number of values."},{"text":"$$\\text{largest value}$","correct":false,"explanation":"The largest value does not determine how many values contributed to the mean. To recover the total, multiply the mean by the number of values."},{"text":"$$\\text{range of values}$","correct":false,"explanation":"The range measures the spread between the largest and smallest values, not the size of the data set. The required multiplier is the number of values."}]},{"id":"a8f4e5f5-8488-4eef-b3f9-641d8ba362d0","cardType":"basic","points":2,"front":"How do you find a single missing value if the mean and all other values are known?","back":"

Calculate the full total (mean $\\times$ count)
Subtract the sum of known values from that total

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

Calculate the full total (mean $\\times$ count)
Subtract the sum of known values from that total

","correct":true,"explanation":"Multiplying the mean by the count reconstructs the total of every value. Removing the sum of the known values then leaves exactly the single missing value."},{"text":"

Calculate the full total (mean $\\div$ count)
Subtract the sum of known values from that total

","correct":false,"explanation":"Dividing the mean by the count reverses the relationship incorrectly and produces no useful total. The full total is mean multiplied by count, followed by subtracting the known sum."},{"text":"

Calculate the full total (mean $\\times$ count)
Add the sum of known values to that total

","correct":false,"explanation":"Adding the known values counts them twice because they are already included in the full total. Their sum must be subtracted from mean multiplied by count."},{"text":"

Calculate the known total (mean $\\times$ count)
Divide the sum of known values by that total

","correct":false,"explanation":"The given mean and count produce the full total, not merely the known total. Subtracting the known sum isolates the missing value; dividing the two totals does not."}]},{"id":"aeaa1401-c9b3-4479-b986-23ddc07adece","cardType":"basic","points":1,"front":"Five cards have a mean of 10. What is their total?","back":"$$10 \\times 5 = 50$","mcqOptions":[{"text":"$$10 \\times 5 = 50$","correct":true,"explanation":"A mean of 10 across five cards gives a total of mean multiplied by count. Therefore, the cards have a combined value of 50."},{"text":"$$10 + 5 = 15$","correct":false,"explanation":"Adding the mean and the number of cards confuses the count with another data value. The total is found by multiplying them: $10 \\times 5 = 50$."},{"text":"$$10 \\div 5 = 2$","correct":false,"explanation":"Dividing by the count is used to calculate a mean from a known total. Here the mean is already known, so multiply by five to obtain 50."},{"text":"$$10 \\times 4 = 40$","correct":false,"explanation":"Using four is an off-by-one counting error because the question states that there are five cards. Multiplying the mean by all five gives $10 \\times 5 = 50$."}]},{"id":"e526582e-562d-4fda-95b2-ca1995737c2b","cardType":"basic","points":3,"front":"How do you calculate the new mean when one more value is added to a set?","back":"

Find the original total
Add the new value
Divide the new total by the new number of values

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

Find the original total
Add the new value
Divide the new total by the new number of values

","correct":true,"explanation":"The added value changes both the total and the count. Adding it to the original total and dividing by the increased count therefore gives the new mean."},{"text":"

Find the original total
Subtract the new value
Divide the new total by the new number of values

","correct":false,"explanation":"Subtracting treats the extra value as though it were removed from the data set. It must be added to the original total before dividing by the new count."},{"text":"

Find the original mean
Add the new value
Divide the new total by the new number of values

","correct":false,"explanation":"A mean cannot be added directly to a new data value because it is not the original total. First reconstruct the total, then add and divide by the new count."},{"text":"

Find the original total
Add the new value
Divide the new total by the original number of values

","correct":false,"explanation":"Keeping the original count ignores that the data set now contains one extra value, making the calculated mean too large. Divide the updated total by the new number of values."}]},{"id":"bdd9c5f3-6c1a-402d-9fce-b6b2d54a1f60","cardType":"basic","points":3,"front":"The mean of 10 scores is 20. The mean of 4 of those scores is 5. How do you find the mean of the remaining 6 scores?","back":"

Find total of all 10 ($20 \\times 10 = 200$)
Find total of the 4 ($5 \\times 4 = 20$)
Subtract to find remaining total ($180$) and divide by 6

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

Find total of all 10 ($20 \\times 10 = 200$)
Find total of the 4 ($5 \\times 4 = 20$)
Subtract to find remaining total ($180$) and divide by 6

","correct":true,"explanation":"The ten scores total 200 and the four-score group totals 20. Their difference is 180, which divided among the remaining six scores gives a mean of 30."},{"text":"

Find total of all 10 ($20 + 10 = 30$)
Find total of the 4 ($5 \\times 4 = 20$)
Subtract to find remaining total ($10$) and divide by 6

","correct":false,"explanation":"Adding the mean and count does not reconstruct the overall total. The total is $20 \\times 10 = 200$, leaving 180 for the six remaining scores."},{"text":"

Find total of all 10 ($20 \\times 10 = 200$)
Find total of the 4 ($5 \\times 4 = 20$)
Add to find remaining total ($220$) and divide by 6

","correct":false,"explanation":"Adding the subgroup total counts those four scores again instead of removing them from the overall total. Subtract 20 from 200, then divide the remaining 180 by six."},{"text":"

Find total of all 10 ($20 \\times 10 = 200$)
Find total of the 4 ($5 \\times 4 = 20$)
Subtract to find remaining total ($180$) and divide by 4

","correct":false,"explanation":"Dividing by four reuses the size of the subgroup that was removed. There are six scores remaining, so their total of 180 must be divided by six."}]},{"id":"f82880c6-c374-41ec-a9b5-c28af208073d","cardType":"cloze","points":null,"front":"The median position for a list of 5 values is the [ ] value once ordered.","back":"The median position for a list of 5 values is the 3rd value once ordered.","mcqOptions":[{"text":"3rd","correct":true,"explanation":"With five ordered values, two lie below the middle and two lie above it. The central value is therefore in the 3rd position."},{"text":"2nd","correct":false,"explanation":"The 2nd value still has one value before it and three after it, so it is not central. The middle of five ordered values is the 3rd."},{"text":"4th","correct":false,"explanation":"The 4th value has three values before it and only one after it, so it is above the centre. The median position is the 3rd."},{"text":"5th","correct":false,"explanation":"The 5th value is the largest value in the ordered list, not the middle value. For five values, the median occupies the 3rd position."}]},{"id":"1cea3172-78d2-4941-9aec-478ef01fbbd0","cardType":"basic","points":1,"front":"In a list of 6 ordered values, which positions are used to find the median?","back":"The 3rd and 4th values.","mcqOptions":[{"text":"The 3rd and 4th values.","correct":true,"explanation":"An even-sized list has no single middle value. In a list of six, the two central positions are 3rd and 4th, and their mean is the median."},{"text":"The 2nd and 5th values.","correct":false,"explanation":"These positions are equally spaced from the ends but are not adjacent at the centre. The middle pair in six ordered values is the 3rd and 4th."},{"text":"The 1st and 6th values.","correct":false,"explanation":"The 1st and 6th positions are the smallest and largest values, which are used to determine the range. The median uses the 3rd and 4th values."},{"text":"The 3rd and 5th values.","correct":false,"explanation":"The 5th position lies above the centre and skips over the actual upper-middle value. For six ordered values, use the adjacent 3rd and 4th positions."}]},{"id":"fc2eb4a0-0074-4e7c-aa04-0ffa532b8f05","cardType":"basic","points":1,"front":"Why is it useful to write down the total in mean calculations?","back":"It helps secure method marks and is necessary for solving missing value questions.","mcqOptions":[{"text":"It helps secure method marks and is necessary for solving missing value questions.","correct":true,"explanation":"Writing the total shows the key step mean multiplied by count, which can earn method marks. A missing value is then found by subtracting the known values from this total."},{"text":"It helps secure accuracy marks and is necessary for solving range questions.","correct":false,"explanation":"The range only needs the largest and smallest values, so the total is unnecessary. Writing the total mainly demonstrates the mean method and supports missing-value calculations."},{"text":"It helps identify the middle position and is necessary for solving median value questions.","correct":false,"explanation":"Median questions depend on ordering the values and locating the middle, not calculating their total. The total is instead useful for method marks and missing-value mean questions."},{"text":"It helps identify the most frequent value and is necessary for solving mode value questions.","correct":false,"explanation":"The mode is identified by counting how often each value appears, so the total is not required. Totals are useful when showing mean methods and finding missing values."}]}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Paper 1"},"heading":"Averages","title":"Averages Flashcards","topbar":{"backHref":"/igcse/maths/edexcel/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"9d76d594-4a4d-496b-a783-d6043f9c99ed","walled":"$L39"}],"$L3a","$L3b"]