Class 10 Maths Chapter 13 (formerly Chapter 14), Statistics, extends measures of central tendency from ungrouped data to grouped frequency distributions: computing the Mean by the Direct, Assumed Mean and Step-Deviation methods, the Mode of grouped data, the Median using cumulative frequency, and the empirical relationship 3 Median = Mode + 2 Mean.
What Class 10 Maths Chapter 13 Covers
13.1 Mean of Grouped Data defines the class mark (mid-point) x_i = Upper class limit + Lower class limit / 2 and derives three equivalent formulas for the mean \bar{x}: (1) Direct Method \bar{x} = \sum f_i x_i / \sum f_i; (2) Assumed Mean Method \bar{x} = a + \sum f_i d_i / \sum f_i where d_i = x_i – a; (3) Step-Deviation Method \bar{x} = a + (\sum f_i u_i / \sum f_i) × h where u_i = x_i – a / h.
13.2 & 13.3 Mode and Median of Grouped Data identifies the modal class (the class interval with maximum frequency f1) to compute Mode = l + (f1 – f0 / 2f1 – f0 – f2) × h; constructs the ‘less than’ cumulative frequency table to locate the median class (whose cumulative frequency is just greater than or equal to n/2) and computes Median = l + (n/2 – cf / f) × h; and connects all three measures via 3 Median = Mode + 2 Mean.
Exercises in Chapter 13
- Exercise 13.1 (9 Questions) computes the mean of grouped data using Direct, Assumed Mean and Step-Deviation methods (including finding a missing frequency f when the mean pocket allowance is Rs 18).
- Exercise 13.2 (6 Questions) finds the mode and mean of hospital patient age data, lifetimes of electrical components, household expenditure, student-teacher ratios and batting scores.
- Exercise 13.3 (7 Questions) computes the median, mean and mode of electricity consumption, finding two missing frequencies x and y given $n = 60$ and Median = 28.5, life insurance policy age tables, leaf lengths (converting discontinuous intervals to continuous by subtracting/adding 0.5), neon lamp lifetimes and surname letter counts.
Read Class 10 Maths Chapter 13 Online
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FAQ
What are the formulas for Mode and Median of grouped data in Class 10 Maths?
Mode = l + (f1 – f0 / 2f1 – f0 – f2) × h, where l is the lower limit of the modal class, f1 its frequency, f0 the preceding frequency and f2 the succeeding frequency. Median = l + (n/2 – cf / f) × h, where l is the lower limit of the median class, f its frequency, and cf the cumulative frequency of the class preceding the median class.
What is the empirical relationship between Mean, Median and Mode?
3 Median = Mode + 2 Mean (or Mode = 3 Median – 2 Mean).