Averages & RangeCambridge IGCSE Maths: Flashcards

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State the formula for the mean.

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State the formula for the mean.: $\text{mean} = \frac{\text{sum of values}}{\text{number of values}}$
How do you find the median of an ordered data set?: It is the middle value; average the two middle values if there is an even number of data points
What is the mode?: The value that occurs most frequently in a data set
State the formula for the range.: $\text{range} = \text{highest value} - \text{lowest value}$
Which average is most affected by outliers?: The mean
Which average works for non-numerical (categorical) data?: The mode
State the formula for the mean from a frequency table.: $\frac{\sum (\text{value} \times \text{frequency})}{\sum \text{frequency}}$
What is the interquartile range (IQR)?: $Q3 - Q1$ , the range of the middle 50% of ordered data
Why is IQR often preferred over range as a measure of spread?: Because it is not affected by extreme outliers, unlike the range
What is the 'modal class' in grouped data?: The class interval with the highest frequency
How do you estimate the mean of grouped data?: Multiply each class midpoint by its frequency, sum these, and divide by the total frequency
Why must the mean of grouped data be called an 'estimate'?: Because the exact individual values within each class are unknown, only the class interval and frequency
Find the median of: 3, 7, 5, 9, 2.: Order first: 2,3,5,7,9 — median is 5
Find the mean, median and mode of: 4, 4, 6, 8, 8, 8, 10.: Mean = 48/7 ≈ 6.86; median = 8; mode = 8