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Chapter Analysis
Intermediate30 pages • EnglishQuick Summary
Chapter 13 of the Class 10 Math textbook delves into the concepts of Statistics, extending the study of mean, median, and mode from ungrouped data to grouped data. The chapter discusses various methods to calculate the mean, including the direct, assumed mean, and step-deviation methods, and explains the determination of the median and mode, particularly in the context of grouped data. Emphasis is laid on the significance and applications of these measures of central tendency in real-life situations. Additionally, the chapter includes discussions on cumulative frequency, cumulative frequency distribution, and how to draw ogives.【4:19†class-10-math-chapter-13.pdf】
Key Topics
- •Mean of grouped and ungrouped data
- •Calculation of median and mode
- •Understanding cumulative frequency
- •Use of cumulative frequency curves (ogives)
- •Step-deviation method for mean
- •Real-life applications of statistical measures
- •Limitations of mean in data representation
- •Selecting appropriate measures of central tendency
Learning Objectives
- ✓Understand the methods to calculate mean, median, and mode for grouped data
- ✓Learn to construct and interpret cumulative frequency curves
- ✓Develop skills to choose appropriate statistical measures for data interpretation
- ✓Apply statistical concepts to solve real-life data problems
- ✓Differentiate between various measures of central tendency and their implications
- ✓Critically analyze the impact of outliers on data representation
Questions in Chapter
The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.
Page 198
If the median of the distribution given below is 28.5, find the values of x and y.
Page 198
A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 year.
Page 198
The lengths of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table. Find the median length of the leaves.
Page 200
The following table gives the distribution of the life time of 400 neon lamps. Find the median life time of a lamp.
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Additional Practice Questions
What is the mean of a series of numbers if the series follows a pattern that each next term is double the previous term, with the first term being 1 and there are 7 terms in total?
mediumAnswer: The series is 1, 2, 4, 8, 16, 32, 64. First, sum the series: 1 + 2 + 4 + 8 + 16 + 32 + 64 = 127. The mean is 127/7, which is approximately 18.14.
If a data set has a mode of 15 and a median of 20, can the mean be 10? Explain.
hardAnswer: No, the mean cannot be 10. Typically, if mode < median < mean, then it suggests that data is positively skewed. Therefore, it does not support mode being 15, median 20, and mean 10.
How does the inclusion of a significantly higher value in a data set affect the mean and median?
mediumAnswer: The inclusion of a significantly higher value in a data set will substantially increase the mean, as the mean is sensitive to extreme values, but the median will change slightly or not at all depending on the number of data points.
For a given data set with an even number of terms, explain how to find the median.
easyAnswer: For an even number of terms, arrange the data in ascending order, find the two middle numbers, and calculate their average. This average is the median.
What is the impact of having a large gap between classes in a frequency distribution on the measure of the mode?
hardAnswer: A large gap can make it difficult to identify a clear modal class, as the distribution of frequencies may not clearly show a peak or may be misleading.