🟩 Class 10 Maths Chapter 14: Statistics – Notes & Blog Post

 

📘 Introduction

Statistics deals with the collection, analysis, interpretation, and presentation of data. This chapter focuses on how to:

• Organize grouped data

• Represent it graphically (histograms, ogives)

• Find mean, median, and mode for grouped data

These are measures of central tendency, which help us understand the data better.

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📊 1. Important Definitions

• Data: Information collected in raw form.

• Class Interval: The range in which data is grouped (e.g., 0–10, 10–20).

• Frequency: Number of times a value appears.

• Class Mark: Midpoint of a class = $\frac{\text{Lower limit + Upper limit}}{2}$

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🔢 2. Mean (Grouped Data)

Mean Formula (Using Assumed Mean method):

$$\bar{x} = a + \frac{\sum fd}{\sum f}$$

Where:

• $a$ = assumed mean

• $f$ = frequency

• $d = x - a$ = deviation

• $x$ = class mark = $\frac{\text{lower limit + upper limit}}{2}$

📌 This method simplifies calculation for large data.

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➗ 3. Median (Grouped Data)

Steps:

1. Find the cumulative frequency (cf).

2. Find the median class: Class with $\frac{N}{2}$ where $N = \sum f$

3. Apply the formula:

$$\text{Median} = l + \left(\frac{\frac{N}{2} - F}{f}\right) \times h$$

Where:

• $l$ = lower boundary of the median class

• $N$ = total frequency

• $F$ = cumulative frequency before median class

• $f$ = frequency of median class

• $h$ = class width

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📈 4. Mode (Grouped Data)

Mode Formula:

$$\text{Mode} = l + \left( \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right) \times h$$

Where:

• $l$ = lower limit of modal class

• $f_1$ = frequency of modal class

• $f_0$ = frequency before modal class

• $f_2$ = frequency after modal class

• $h$ = class width

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📉 5. Graphical Representation

• Histogram: Bars representing class intervals vs frequency.

• Frequency Polygon: Line graph joining midpoints of histogram bars.

• Ogives:

  • Less than Ogive: Plot cumulative frequencies from lower limits.

  • More than Ogive: Plot from upper limits.

📌 Intersection of less than and more than ogive gives median.

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💡 Example Problems

Q1. Calculate the mean of the following data:

✅ Use class marks and assumed mean method to solve.

Q2. Find the median of this data:

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📝 Key Points to Remember

• Use class marks for mean calculation.

• Median = middle value, useful in skewed distributions.

• Mode = most frequent value; helps identify trends.

• Graphical methods enhance understanding.

• Mean < Median < Mode (in left-skewed data) or Mean > Median > Mode (in right-skewed).

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📚 Summary Table

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