Mathematics, Statistics & Data Science
High School (11–12)
Statistics and Probability › StatisticsChapter 17Statistics
Two classes both have an average mark of 60. In one class every student scored close to 60. In the other, some scored 20 and some scored 100. The average alone cannot tell them apart. This chapter gives you the numbers that can: the range, the mean deviation, the variance and the standard deviation. Then you compare data sets, combine them, read quartiles and box plots, and measure how two quantities move together with correlation and regression. It covers the statistics unit of the Indian syllabus (NCERT, JEE Main) and the matching topics of A-Level, IB, AP Statistics and the SAT. Python checks every figure on the computer.
Part of Mathematics · High School (11–12) (chapter 17)
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Centre and Spread of Data
A weather office reports the average temperature of a town, but a farmer also wants to know how much the temperature jumps from day to day. Start with the three averages: the mean, the median and the mode, for a short list, a frequency table and grouped data. Then measure the spread with the range, the mean deviation, the variance and the standard deviation. The shortcut and step-deviation methods save work on big tables. It covers the first part of the Indian syllabus unit (NCERT, JEE Main) and the matching topics of A-Level, IB and AP.
Comparing and Combining Data
Which of two bowlers is more consistent, when one takes more wickets on average? Which batch of bulbs is steadier? The standard deviation alone cannot answer, because it depends on the size of the numbers. Use the coefficient of variation to compare. See what happens to the mean and the spread when every value changes, and how to combine two groups, or correct a wrong reading, without starting again. Finish with quartiles, box plots and the rule for outliers. It covers the second part of the Indian syllabus unit (NCERT, JEE Main) and the matching topics of A-Level, IB and AP.