‘रचना-प्रयोग’ का मुख्य उद्देश्य क्या है?

व्याकरण का व्यावहारिक प्रयोग सिखाना

‘द्वितीयः’ किस प्रकार की संख्या है?

क्रमवाचक (दूसरा)

State the empirical relationship between mean, median and mode.

\(\text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean}\).

Name three methods to find the mean of grouped data.

Direct method, assumed-mean method, and step-deviation method.

Name the three measures of central tendency.

The mean, the median and the mode.

Name the methods of finding the mean of grouped data.

The direct method, the assumed-mean (deviation) method and the step-deviation method.

Write the formula for the median of grouped data.

\(\text{Median} = l + \dfrac{\frac{n}{2} - cf}{f} \times h\), where \(l\) is the lower limit of the median class, \(cf\) the cumulative frequency before it, \(f\) its frequency and \(h\) the class size.

Write the formula for the mode of grouped data.

\(\text{Mode} = l + \dfrac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h\), using the modal class and the frequencies around it.

State the empirical relationship between mean, median and mode.

\(\text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean}\).

The mean of 5 numbers is 18. If one number is removed, the mean becomes 16. Find the removed number.

Sum of 5 numbers \(= 90\); sum of 4 numbers \(= 64\); so the removed number \(= 90 - 64 = 26\).

What is a cumulative frequency?

The running total of the frequencies up to a given class, used to draw an ogive and to find the median.

What does an ogive help to find?

The median of grouped data graphically, as the x-coordinate of the point where the two cumulative frequency curves meet (or where \(cf = n/2\)).

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Chapter 13: StatisticsClass 10 Mathematics — summary, notes, extra questions & NCERT solutions

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The most frequently occurring value in a data set is the:

Summary

Statistics deals with collecting, organising and interpreting numerical data. This chapter focuses on measures of central tendency for grouped data — the mean (using the direct, assumed-mean or step-deviation method), the median (using the median class and its formula) and the mode (using the modal class formula). It also explains the relationship \(\text{Mode} = 3\,\text{Median} - 2\,\text{Mean}\). These measures summarise a large data set with a single representative value, which is essential for comparing and drawing conclusions from data.

Mean of grouped dataMedian of grouped dataMode of grouped dataRelationship between mean, median and mode

Key terms

Mean

The average value of the data.

Median

The middle value that divides ordered data into two halves.

Mode

The most frequently occurring value (or modal class).

Empirical relationship

\(\text{Mode} = 3\,\text{Median} - 2\,\text{Mean}\).

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EXERCISE 13.1

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Mean, median and mode

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Mode

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The average value of the data.

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Chapter 13: StatisticsClass 10 Mathematics — summary, notes, extra questions & NCERT solutions

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Key terms

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EXERCISE 13.1

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