📘 Statistics Class 10 Notes (Chapter 14)

🔷 Introduction

Statistics helps us collect, organize, and study data. In simple words, statistics turns numbers into useful information. Therefore, students can understand large sets of data more easily.

Moreover, people use statistics in schools, business, sports, science, and research. As a result, this chapter has many real-life uses.

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🔷 What is Data?

Data means a collection of facts, numbers, or observations.

For example, marks of students, daily temperatures, or cricket scores all form data. Thus, data helps us compare and analyze information.

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🔷 Types of Data

Understanding data types makes this chapter easier. Therefore, learn these types carefully.

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✔ Raw Data

Raw data is the original data collected directly.

For example:

12, 15, 10, 18, 14, 16

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✔ Grouped Data

Grouped data organizes values into classes.

For example:

Class Interval	Frequency
0–10	5
10–20	8
20–30	6

Thus, grouped data looks clean and easy to study.

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🔷 Frequency

Frequency shows how many times a value appears.

For example, if 10 appears three times, then frequency = 3.

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🔷 Class Interval

A class interval shows a range of values.

For example:

10–20, 20–30, 30–40

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🔷 Class Mark

Class mark is the middle value of a class interval.

Formula:$$Class\ Mark=\frac{Upper\ Limit+Lower\ Limit}{2}$$Class Mark=2Upper Limit+Lower Limit​

Therefore, class mark helps in calculations.

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🔷 Mean

Mean gives the average value of data.

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Formula for Ungrouped Data

$$Mean=\frac{Sum\ of\ observations}{Number\ of\ observations}$$Mean=Number of observationsSum of observations​

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Formula for Grouped Data

$$\bar{x}=\frac{\sum f_ix_i}{\sum f_i}$$xˉ=∑fi​∑fi​xi​​

Where:

• $f_i$fi​ = frequency
• $x_i$xi​ = class mark

Thus, mean shows the central value.

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🔷 Assumed Mean Method

Sometimes numbers become large. Therefore, we use the assumed mean method.

Formula:$$\bar{x}=a+\frac{\sum f_id_i}{\sum f_i}$$xˉ=a+∑fi​∑fi​di​​

Where:

• $a$a = assumed mean
• $d_i=x_i-a$di​=xi​−a

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🔷 Step Deviation Method

This method makes calculations easier. Moreover, it saves time in exams.

Formula:$$\bar{x}=a+\frac{\sum f_iu_i}{\sum f_i}\times h$$xˉ=a+∑fi​∑fi​ui​​×h

Where:

• $u_i=\frac{x_i-a}{h}$ui​=hxi​−a​

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🔷 Median

Median is the middle value of data.

Therefore, median divides data into two equal parts.

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Formula of Median

$$Median=l+\left(\frac{\frac n2-cf}{f}\right)\times h$$Median=l+(f2n​−cf​)×h

Where:

• $l$l = lower boundary
• $n$n = total frequency
• $cf$cf = cumulative frequency
• $f$f = frequency
• $h$h = class size

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🔷 Mode

Mode is the value with highest frequency.

In other words, mode shows the most common observation.

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Formula of Mode

$$Mode=l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h$$Mode=l+(2f1​−f0​−f2​f1​−f0​​)×h

Where:

• $f_1$f1​ = modal class frequency
• $f_0$f0​ = previous frequency
• $f_2$f2​ = next frequency

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🔷 Empirical Relation

This relation connects mean, median, and mode.

Formula:$$Mode=3Median-2Mean$$Mode=3Median−2Mean

Therefore, this formula helps verify answers.

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🔷 Solved Example

Example

Find the mean of:

5, 7, 9, 11, 13

Solution

Sum:$$5+7+9+11+13=45$$5+7+9+11+13=45

Number of observations:$$5$$5

Now use:$$Mean=\frac{45}{5}$$Mean=545​ $$Mean=9$$Mean=9

Answer:

Mean = 9

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🔷 Important Tips

Students can score full marks by following these tips.

• Make tables carefully.
• Check frequencies twice.
• Write formulas first.
• Solve step by step.
• Always write units if needed.

Thus, neat work improves accuracy.

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🔷 Real-Life Uses

People use statistics in many fields. For example, statistics helps in:

• School results
• Cricket analysis
• Business reports
• Medical research
• Population studies
• Weather reports

Therefore, statistics plays an important role in daily life.