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In a histogram the area of each rectangle is proportional to
- a)the class size of the corresponding class interval
- b)cumulative frequency of the corresponding class interval
- c)the class mark of the corresponding class interval
- d)frequency of the corresponding class interval
Correct answer is option 'D'. Can you explain this answer?
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In a histogram the area of each rectangle is proportional toa)the clas...
A histogram is a display of statistical information that uses rectangles to show the frequency of data items in successive numerical intervals of equal size. In the most common form of histogram, the independent variable is plotted along the horizontal axis and the dependent variable is plotted along the vertical axis.
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In a histogram the area of each rectangle is proportional toa)the clas...
In a histogram, the area of each rectangle is proportional to the frequency of the corresponding class interval.
Understanding a Histogram:
A histogram is a graphical representation of data that is grouped into intervals or classes. It consists of a series of rectangles, where the height of each rectangle represents the frequency (or number of occurrences) of data falling within a particular class interval.
Explanation:
To understand why the area of each rectangle in a histogram is proportional to the frequency, let's break it down step by step:
1. Class Intervals:
When data is collected, it is often grouped into intervals or classes to make it more manageable. These intervals represent a range of values. For example, if we are collecting data on the heights of students, we may have class intervals like 150-160 cm, 160-170 cm, etc.
2. Frequency:
The frequency of a class interval refers to the number of data points that fall within that interval. It represents how many times a particular value or range occurs in the data set.
3. Rectangle Height:
In a histogram, the height of each rectangle corresponds to the frequency of the corresponding class interval. The taller the rectangle, the higher the frequency of data falling within that interval.
4. Rectangle Width:
The width of each rectangle is determined by the class interval. The width represents the range of values covered by the interval. The wider the interval, the wider the rectangle.
5. Area Calculation:
To calculate the area of a rectangle, we multiply its height by its width. In the case of a histogram, the area of each rectangle is proportional to both the frequency (height) and the class interval (width). However, since the width is the same for all rectangles in a histogram, it cancels out when comparing the areas of different rectangles.
6. Proportional Area:
Therefore, the only remaining factor that determines the area of each rectangle is the frequency. The larger the frequency, the larger the area of the rectangle. This proportionality allows us to visually compare the frequencies of different class intervals in the histogram.
Conclusion:
In conclusion, the area of each rectangle in a histogram is proportional to the frequency of the corresponding class interval. This property enables us to visually represent and compare the distribution of data across different intervals in a graphical and intuitive manner.
Understanding a Histogram:
A histogram is a graphical representation of data that is grouped into intervals or classes. It consists of a series of rectangles, where the height of each rectangle represents the frequency (or number of occurrences) of data falling within a particular class interval.
Explanation:
To understand why the area of each rectangle in a histogram is proportional to the frequency, let's break it down step by step:
1. Class Intervals:
When data is collected, it is often grouped into intervals or classes to make it more manageable. These intervals represent a range of values. For example, if we are collecting data on the heights of students, we may have class intervals like 150-160 cm, 160-170 cm, etc.
2. Frequency:
The frequency of a class interval refers to the number of data points that fall within that interval. It represents how many times a particular value or range occurs in the data set.
3. Rectangle Height:
In a histogram, the height of each rectangle corresponds to the frequency of the corresponding class interval. The taller the rectangle, the higher the frequency of data falling within that interval.
4. Rectangle Width:
The width of each rectangle is determined by the class interval. The width represents the range of values covered by the interval. The wider the interval, the wider the rectangle.
5. Area Calculation:
To calculate the area of a rectangle, we multiply its height by its width. In the case of a histogram, the area of each rectangle is proportional to both the frequency (height) and the class interval (width). However, since the width is the same for all rectangles in a histogram, it cancels out when comparing the areas of different rectangles.
6. Proportional Area:
Therefore, the only remaining factor that determines the area of each rectangle is the frequency. The larger the frequency, the larger the area of the rectangle. This proportionality allows us to visually compare the frequencies of different class intervals in the histogram.
Conclusion:
In conclusion, the area of each rectangle in a histogram is proportional to the frequency of the corresponding class interval. This property enables us to visually represent and compare the distribution of data across different intervals in a graphical and intuitive manner.
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In a histogram the area of each rectangle is proportional toa)the class size of the corresponding class intervalb)cumulative frequency of the corresponding class intervalc)the class mark of the corresponding class intervald)frequency of the corresponding class intervalCorrect answer is option 'D'. Can you explain this answer?
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