Statistics

This chapter finds the three measures of central tendency — mean, median and mode — for grouped data. For the mean it develops all three methods: the direct method $\bar{x}=\frac{\sum f_ix_i}{\sum f_i}$, the assumed-mean method and the step-deviation method. It then gives the mode of grouped data from the modal class, and the median from the cumulative frequency and the median class. Finally it introduces the cumulative frequency distribution and its graph, the ogive (less-than and more-than types), shows how to read the median from an ogive, and states the empirical relationship $3\,\text{Median}=\text{Mode}+2\,\text{Mean}$. It is a formula-driven, high-scoring chapter of the Class 10 Board syllabus.