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The mean and the standard deviation of a set of data are descriptive statistics usually reported together. In a certain sense, the standard deviation is a "natural" measure of statistical dispersion if the center of the data is measured about the mean. This is because the standard deviation from the mean is smaller than from any other point.
For an approximately normal data set, the values within one standard deviation of the mean account for about 68% of the set; while within two standard deviations account for about 95%; and within three standard deviations account for about 99.7%. Shown percentages are rounded theoretical probabilities intended only to approximate the empirical ...
AQA Education, [1] trading as AQA (formerly the Assessment and Qualifications Alliance), is an awarding body in England, Wales and Northern Ireland. It compiles specifications and holds examinations in various subjects at GCSE, AS and A Level and offers vocational qualifications. AQA is a registered charity and independent of the government.
Additional Mathematics is a qualification in mathematics, commonly taken by students in high-school (or GCSE exam takers in the United Kingdom). It features a range of problems set out in a different format and wider content to the standard Mathematics at the same level.
At one point in time, the “A*” grade in the GCSE did not exist but was later added to recognise the very top end of achievement. In the case of Further Mathematics, an extra A* grade was added for students that can “demonstrate sustained performance in higher-level maths skills such as reasoning, proof and problem-solving.” [14]
Each GCSE qualification is offered as a specific school subject, with the most commonly awarded ones being: English literature, English language, mathematics, science (double & triple), history, geography, art, design and technology (D&T), business studies, economics, music, and modern foreign languages (E.g. Spanish, French, German) (MFL).
Bias in standard deviation for autocorrelated data. The figure shows the ratio of the estimated standard deviation to its known value (which can be calculated analytically for this digital filter), for several settings of α as a function of sample size n. Changing α alters the variance reduction ratio of the filter, which is known to be
Since the square root introduces bias, the terminology "uncorrected" and "corrected" is preferred for the standard deviation estimators: s n is the uncorrected sample standard deviation (i.e., without Bessel's correction) s is the corrected sample standard deviation (i.e., with Bessel's correction), which is less biased, but still biased