Chapter 13 — Statistics

NCERT Class 10 Maths Chapter 13 covers Statistics, extending the study of mean, median, and mode from ungrouped data to grouped data, and introducing cumulative frequency distributions and ogives.

Chapter 13 of NCERT Class 10 Mathematics extends the measures of central tendency — mean, median, and mode — to grouped data. It introduces three methods for calculating the mean of grouped data: the Direct Method, the Assumed Mean Method, and the Step-Deviation Method, all yielding identical results. The mode of grouped data is found using the modal class formula, while the median is determined by locating the median class from cumulative frequency tables. The chapter also covers 'less than' and 'more than' type cumulative frequency distributions and their graphical representation as ogives. An empirical relationship links the three measures: 3 Median = Mode + 2 Mean.

1. 01Three methods — Direct, Assumed Mean, and Step-Deviation — are used to find the mean of grouped data and always give the same result.
2. 02The mode of grouped data is calculated using the formula Mode = l + [(f1 − f0) / (2f1 − f0 − f2)] × h, where the modal class has the highest frequency.
3. 03The median of grouped data is found using Median = l + [(n/2 − cf) / f] × h, after identifying the median class from the cumulative frequency table.
4. 04Cumulative frequency distributions can be of the 'less than' type (using upper class limits) or 'more than' type (using lower class limits).
5. 05The empirical relationship between the three measures of central tendency is: 3 Median = Mode + 2 Mean.
6. 06Mean is best when all observations matter; median suits skewed data or typical values; mode identifies the most frequent value.