Chapter 13 — Statistics

Chapter 13 of the Class 10 Maths NCERT textbook, "Statistics", extends the study of mean, median, and mode from ungrouped to grouped data, and introduces cumulative frequency distributions and their graphs, called ogives.

• Three ways to find the mean — For grouped data the mean can be found by the Direct, Assumed Mean, or Step-Deviation method. All three give the same answer, with the shortcuts easing arithmetic when the numbers are large.
• Mode and median for grouped data — The mode is read from the modal class with the highest frequency, and the median from the median class located using a cumulative frequency table — each computed with its own formula.
• Cumulative frequency and ogives — Cumulative frequencies of the 'less than' or 'more than' type can be plotted as smooth curves called ogives. An empirical rule, 3 Median = Mode + 2 Mean, links the three averages.

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.