AQA · Mathematics · 8300
GCSE Maths: Averages: mode
Statistics · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise, practice questions and answers for Averages: mode (Corbettmaths Video 56), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
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If a dataset has 11 values and a median of 1.85m, with only one value equal to 1.85m, how many values are below 1.85m?
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5 values. With 11 values, the median is the 6th value. If that's 1.85m, then 5 values must be below it.
If the range of a dataset is 7 and the smallest value is 4, what is the largest value?
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11. Since range = largest − smallest, we have 7 = largest − 4, so largest = 11.
If five numbers have a mean of 8, what is the sum of those five numbers?
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40. Since mean = sum ÷ number of values, we have 8 = sum ÷ 5, so sum = 40.
If the mean of four numbers is 10 and three of them are 9, 11, and 7, what is the fourth number?
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13. Total sum needed = 4 × 10 = 40. Sum of three numbers = 9 + 11 + 7 = 27. Fourth number = 40 − 27 = 13.
When finding the median of an even number of values, how do you determine it?
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Find the two middle values and calculate their mean (average).
If a team has played 5 matches with a mean of 3 goals, and after the 6th match the mean increases to 4, how many goals were scored in the 6th match?
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9 goals. Total after 5 matches = 5 × 3 = 15. Total after 6 matches = 6 × 4 = 24. Goals in 6th match = 24 − 15 = 9.
Define the mode of a data set.
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The value that appears most frequently in the data set.
Define the median of a data set.
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The middle value when the data is arranged in order from smallest to largest.
Define the range of a data set.
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The difference between the largest and smallest values in the data set.
Define the mean of a data set.
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The sum of all values divided by the number of values.
What must you do to a data set before finding the median?
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Arrange the values in order from smallest to largest.
How does the range of a data set change when the same number is added to every value?
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The range stays the same because the difference between largest and smallest values does not change.
When is the mean not the most suitable average to summarize a data set?
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When there are outliers or extreme values that skew the data.
If a data set has 7 values arranged in order, which position is the median?
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The 4th value (the middle position).
How do you calculate range when dealing with negative numbers?
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Subtract the smallest value from the largest value (e.g., 5 − (−8) = 13).
How do you calculate a new mean when one more value is added to a data set?
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Calculate the total of the original values (old mean × count), add the new value, then divide by the new count.
To find the total needed for a target mean, what calculation do you use?
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Multiply the target mean by the number of values.
The ? is the value that appears most frequently in a data set.
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