Statistics ToolkitEdexcel IGCSE Maths: Flashcards

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What is the formula for the mean of a data set?

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What is the formula for the mean of a data set?: $\bar{x} = \dfrac{\sum x}{n}$ — the sum of all values divided by the number of values.
How do you find the median of a data set?: Order the data from smallest to largest. If $n$ is odd, the median is the middle value. If $n$ is even, it is the mean of the two middle values.
What is the mode?: The value that occurs most frequently in a data set. A data set can have no mode, one mode, or more than one mode.
How is the range calculated?: Range = largest value − smallest value. It is a single number, not an interval.
What is the formula for the mean using a frequency table?: $\bar{x} = \dfrac{\sum fx}{\sum f}$ where $x$ is each data value and $f$ is its frequency.
Why can we only estimate the mean of grouped data?: Because the exact individual values within each class interval are unknown — we assume they all equal the midpoint, which is an approximation.
How do you calculate the midpoint of a class interval?: $\text{midpoint} = \dfrac{\text{lower bound} + \text{upper bound}}{2}$
What is the formula for the estimated mean of grouped data?: $\text{estimated mean} = \dfrac{\sum fx}{\sum f}$ where $x$ is the midpoint of each class and $f$ is the frequency.
What is the modal class?: The class interval with the highest frequency in a grouped frequency table.
What is the median class?: The class interval containing the middle value(s) of the data set, found using cumulative frequency.
How do you locate the median class using cumulative frequency?: Find the position of the middle value (around $\frac{n}{2}$ ), then use the cumulative frequency column to see which class interval that position falls into.
How should you state a modal class or median class in an answer?: As the full class interval, e.g. " $160 \le h < 170$ ", never as a single midpoint value.
When comparing two distributions, what two things must you comment on?: One comment on average (mean, median or mode) and one comment on spread (range or interquartile range), both written in context.
Why might range alone be misleading when comparing spread?: Range only uses the two extreme values, so a single outlier can make the range large even if most data is closely clustered — interquartile range is more robust.
For the data 3, 5, 5, 8, 9, what are the mean, median, mode and range?: Mean = $\dfrac{30}{5} = 6$ ; median = 5 (middle value); mode = 5; range = $9 - 3 = 6$ .