Maths: Analysis and Approaches · Statistics and probability. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
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A set of data is summarised by a measure of centre (mean, median or mode) and a measure of spread (range, interquartile range, standard deviation or variance). The standard deviation shows how far the values are from the mean on the whole, and the variance is its square.
For grouped data the exact values are lost, so the mean is an estimate found from the class midpoints.
You also read these measures from diagrams. On a cumulative frequency graph, the median is at half the total frequency and the quartiles are at one quarter and three quarters. On a box-and-whisker plot, the box runs from Q1 to Q3 and the whiskers reach the smallest and largest values.
Students add the constant to the standard deviation as well as to the mean. Adding a number moves every value by the same amount, so the spread stays the same; only multiplying changes it.
Answer: Standard deviation = 2.83 (3 significant figures).
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