Statistics Online Practice Worksheet

Class 10 Statistics Chapter 13 – Complete Practice Guide

Statistics is an important part of Class 10 Mathematics because it teaches students how to organise, interpret and summarise numerical information. Chapter 13 extends the Class 9 work on measures of central tendency from individual observations to grouped data. The main focus is on finding and interpreting the mean, mode and median of grouped distributions. It also introduces cumulative frequency and the idea of cumulative-frequency curves, or ogives. These are the concepts used by this DigiSadhan worksheet to create practice questions.

1. Mean of Grouped Data

When a distribution is grouped into class intervals, a class mark is used as the representative value of each interval. The class mark is the average of the lower and upper class limits. If the class mark is xᵢ and its frequency is fᵢ, the direct method uses the total of fᵢxᵢ divided by the total frequency. This is particularly useful when the class marks and products are easy to calculate.

2. Assumed Mean Method

For larger class marks, calculation can be simplified by selecting a convenient class mark as an assumed mean a. The deviation is dᵢ = xᵢ − a. After multiplying each deviation by its frequency, the mean is obtained by adding the average deviation to the assumed mean. This method gives the same answer as the direct method but can reduce arithmetic work.

3. Step-Deviation Method

If the class intervals have a common width, the step-deviation method can make the arithmetic even shorter. Let h be the class size and define uᵢ = (xᵢ − a)/h. The mean is then found from the weighted average of the coded deviations. Students should carefully keep track of the chosen assumed mean and class size.

4. Mode of Grouped Data

The mode is associated with the observation that occurs most often. In grouped data, first identify the modal class, which is the class having the highest frequency. The formula uses the lower boundary l of the modal class, its class size h, the modal-class frequency f₁, and the frequencies of the preceding and succeeding classes, f₀ and f₂. Before applying the formula, class intervals should be made continuous when necessary.

5. Median of Grouped Data

The median divides a distribution into two equal parts. For grouped data, students first calculate cumulative frequencies and locate the median class, the class whose cumulative frequency first becomes greater than or equal to n/2. Then substitute the lower boundary l, class size h, frequency f of the median class and cumulative frequency cf immediately before it.

6. Cumulative Frequency and Ogive

Cumulative frequency is obtained by successively adding frequencies. In a less-than cumulative frequency table, each entry represents the number of observations below the corresponding upper limit. In a more-than table, frequencies are accumulated from the opposite direction. These values can be used to construct cumulative-frequency curves called ogives. Reading a graph accurately requires suitable scales and correctly labelled axes.

7. Empirical Relationship

For distributions where the standard empirical relationship is applicable, mean, median and mode are connected by a simple relation. It can be rearranged to find one measure when the other two are known. In examination questions, always substitute the given values carefully and check whether the requested measure is reasonable.

8. How to Use This Online Worksheet

Choose the number of questions, question type, difficulty and timer, then press Start New Test. The questions are generated when the test starts, so the worksheet does not depend on a fixed repeated question list. Press Shuffle Whole Worksheet to generate a new set. Every generated question receives a unique internal signature for that worksheet, helping prevent duplicate questions. Type your numerical answer and select Check Answer. A correct answer turns the answer box green and a wrong answer turns it red. The answer is deliberately hidden until the question has been checked, so students can practise honestly.

9. Exam Preparation Tips

For mean questions, make a clear table containing class interval, class mark, frequency and the required products or deviations. For mode questions, do not confuse the modal class with the mode itself. For median questions, calculate cumulative frequency carefully before identifying the median class. Pay attention to continuous class boundaries, especially when the data is given in inclusive intervals such as 10–19, 20–29 and so on. Keep units consistent, write the formula before substitution and round only at an appropriate final step. For application questions, read what the data represents before interpreting the result. A mean may describe an average, while a mode may identify the most common value or class. Median is useful when the central position of ordered data is important.

10. DigiSadhan Practice Features

This worksheet is designed for repeated practice on mobile, tablet and desktop screens. Students can select a small practice set for quick revision or a much larger set for intensive preparation. The progress bar shows completion, while the score and accuracy counters update after each checked response. Correct and incorrect responses include optional sound and lightweight animations. At the end of a test, the result panel shows the score and accuracy. The Save as PDF and Print controls are separate, making the worksheet useful both as an online activity and as a printable revision sheet.

Chapter Coverage

This practice tool follows the Class 10 NCERT Statistics chapter structure: introduction to grouped data, mean of grouped data through direct/assumed-mean/step-deviation methods, mode of grouped data, median of grouped data, cumulative frequency and related interpretation. The official NCERT contents list Chapter 13 as Statistics and its sections as Introduction, Mean of Grouped Data, Mode of Grouped Data, Median of Grouped Data and Summary. citeturn0search24turn1search0