Formula for variance and standard deviation?

Variance =\frac{S{xx}}{n}; standard deviation =\sqrt{\frac{S{xx}}{n}} (using n-1 is also accepted).

What is the 10th to 90th interpercentile range?

The 90th percentile minus the 10th percentile; it covers the middle 80\% of the data.

Linear interpolation formula for a percentile?

L+\frac{position-F{below}}{f}\times w

If y=\frac{x-a}{b}, how is the SD of x found?

SD of x=b\times SD of y (the shift a has no effect).

Effect of adding a constant on mean and SD?

The mean changes by the constant; the SD is unchanged.

Why use the IQR rather than the range?

It is not affected by extreme values.

Measures of location and spreadEdexcel A-Level Maths: Flashcards

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Question

Formula for the mean from a frequency table?

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Formula for the mean from a frequency table?: $\bar x=\frac{\sum fx}{\sum f}$
Which value represents a class when estimating the mean?: The class midpoint.
Formula for $S_{xx}$ ?: $\sum x^2-\frac{(\sum x)^2}{n}$
Formula for variance and standard deviation?: Variance $=\frac{S_{xx}}{n}$ ; standard deviation $=\sqrt{\frac{S_{xx}}{n}}$ (using $n-1$ is also accepted).
Alternative formula for variance?: $\frac{\sum x^2}{n}-\bar x^2$
Define the interquartile range.: $Q_3-Q_1$ .
What is the 10th to 90th interpercentile range?: The 90th percentile minus the 10th percentile; it covers the middle $80\%$ of the data.
Position of the $p$ th percentile for $n$ values?: $\frac{p}{100}\times n$ .
Linear interpolation formula for a percentile?: $L+\frac{\text{position}-F_{\text{below}}}{f}\times w$
If $y=\frac{x-a}{b}$ , how do you find $\bar x$ ?: $\bar x=b\bar y+a$ .
If $y=\frac{x-a}{b}$ , how is the SD of $x$ found?: SD of $x=b\times$ SD of $y$ (the shift $a$ has no effect).
Effect of adding a constant on mean and SD?: The mean changes by the constant; the SD is unchanged.
Why use the IQR rather than the range?: It is not affected by extreme values.

Exam questions on Measures of location and spread

The delivery times, $x$ minutes, of 10 parcels have $\sum x=240$ and $\sum x^2=6100$ .
Calculate the standard deviation of the delivery times.2 marks
A sample of 8 masses, $x$ grams, is coded using $y=\frac{x-400}{10}$ . The coded data have $\sum y=24$ and $\sum y^2=130$ .
A second sample is formed by adding 5 g to every mass in this sample. State the effect on (i) the mean and (ii) the standard deviation.2 marks
A clinic records the waiting times of 50 patients, in minutes: 4 patients waited from 0 up to 10, 12 from 10 up to 20, 20 from 20 up to 30 and 14 from 30 up to 50.
Estimate the mean waiting time.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).