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HIstogram

A histogram is a statistical graph that represents the distribution of continuous data using bars that touch each other, with each bar indicating a range of data and its height showing frequency. Histograms are used to analyze data grouped into intervals, understand distribution shapes, and compare data concentrations. There are various types of histograms, including uniform, symmetrical, skewed, bimodal, and irregular, each representing different data characteristics.

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29 views3 pages

HIstogram

A histogram is a statistical graph that represents the distribution of continuous data using bars that touch each other, with each bar indicating a range of data and its height showing frequency. Histograms are used to analyze data grouped into intervals, understand distribution shapes, and compare data concentrations. There are various types of histograms, including uniform, symmetrical, skewed, bimodal, and irregular, each representing different data characteristics.

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Tayebur
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Histograms – Notes

🔹 What is a Histogram?

A histogram is a type of graph used in statistics to represent the distribution of continuous


data. It looks like a bar graph but has important differences:

 Each bar represents a range (class interval) of data.

 The height of the bar shows the frequency (how many values fall within that range).

 Unlike bar charts, bars in histograms touch each other, because the data is continuous.

🔹 When Do We Use Histograms?

 When data is grouped into intervals (like ages, marks, heights).

 To understand the shape of the data distribution — whether it’s symmetrical, skewed,
or has outliers.

 To compare data concentration across ranges.

🟨 Parts of a Histogram

 X-axis (horizontal): Class intervals or bins (e.g., 0–10, 10–20, etc.)

 Y-axis (vertical): Frequency (number of values in each interval)

 Bars: Represent frequencies for each interval (height = frequency)

🟩 Types of Histograms

✅ 1. Uniform Histogram

 All bars are roughly the same height.

 Data is evenly distributed.

 Example: Equal number of students scoring in each range of marks.

✅ 2. Symmetrical (Bell-Shaped) Histogram

 Data is evenly distributed around a central value.


 The left and right sides are mirror images.

 Often indicates a normal distribution.

 Example: Heights of a large group of people.

✅ 3. Skewed Histogram

 Skewed Right (Positive Skew):


Most data is on the left; tail extends to the right.
Example: Income distribution in a population.

 Skewed Left (Negative Skew):


Most data is on the right; tail extends to the left.
Example: Age at retirement (most people retire around the same age, few much
earlier).

✅ 4. Bimodal Histogram

 Two peaks (modes) appear in the data.

 Suggests the data might come from two different groups.

 Example: Test scores of two different classes on the same exam.

✅ 5. Random or Irregular Histogram

 Bars have no clear pattern.

 May indicate randomness or poorly grouped data.

 Example: Rolling a dice multiple times and recording total values from combinations.

📌 Quick Summary Table


Histogram Type Shape Example

Uniform Equal bar heights Equal number of items per group

Symmetrical (Bell) Central peak, even sides Height distribution

Skewed Right Tail to the right Income distribution

Skewed Left Tail to the left Retirement age

Bimodal Two peaks Two student groups

Irregular/Random No pattern Dice roll data

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