Histogram - class-XI

A histogram is a graphical representation of continuous data where the area of each rectangle is proportional to the frequency of the class interval, and there are no gaps between the bars.

A histogram is a type of frequency diagram because it displays the frequency distribution of a continuous variable.

Histograms and bar diagrams differ in that histograms are for continuous data (no gaps), while bar diagrams are for discrete data (with gaps). Additionally, the width of bars in a histogram represents the class interval, whereas in a bar diagram, width is arbitrary.

Histograms are specifically designed to represent continuous grouped frequency distributions where the data is organized into intervals.

The mode of a continuous frequency distribution can be determined graphically using a histogram by identifying the tallest bar and using specific geometric constructions within that interval.

Histograms are the standard graphical tool for representing continuous frequency distributions.

Despite the typo 'frequents' instead of 'frequency', the statement remains true. A histogram provides a graphical presentation of a continuous frequency distribution using adjacent bars. The error doesn't change the correct answer.

When in a frequency distribution class widths are not same we have to draw histogram then,We find the proportionate lengths of the class corresponding to minimum width and draw the rectangle.
Answer (C) We find the proportionate lengths of the class corresponding to minimum width and draw the rectangle.

A histogram serves as the foundation for constructing other frequency-based visualizations like frequency polygons and frequency curves.

In a histogram with equal class intervals, the area of the rectangle is proportional to the frequency. Since the width is constant, the height must be proportional to the frequency.

Classification is the process of arranging data into groups or classes based on common characteristics, which applies to both quantitative (numerical) and qualitative (categorical) data.

The data shows cumulative frequencies (5, 18, 25) for increasing upper boundaries (10, 30, 50), which is the definition of a 'less than' cumulative frequency distribution.

A histogram is the appropriate choice for displaying continuous grouped frequency distribution data measuring physical fitness. Histograms are specifically designed for continuous data organized into class intervals, which is typical for physical fitness measurements like height, weight, or endurance scores.

Answer:- B) Histogram

The histograms are diagrams which represent the class interval and the frequency in the form of a rectangle. 

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.

Answer:-

Histogram represents grouped data 

Appropriate diagram to represent given data is histogram because histogram easily represents graph of 2 different district on the same graph & in easy to understand graph

Option C is not correct & all other are correct from our basic knowledge of statistics

Using these we can vary one component only

All are the types of histogram

$\Rightarrow$  Histogram is classified as one dimensional diagrams because only $Legth,is,considered.$

$\Rightarrow$  Sum of all components in normalized histogram is equal to $1$

Probablity of a function is always greater than 0 i.e. positive

PDF in histogram equalization stands for probability density function. 

In local histogram we deal with slice of images

A strictly monotonic function is always injective (one-to-one). This ensures that for every output in the range, there is exactly one corresponding input in the domain, making the inverse mapping single-valued.

Well known from application of histogram

It is fundamental concept that a statistical data can be represented using plotting graph between different variable, pie chart, histogram, frequency polygon or frequency table or ogives.
Hence, $A,B,C$ are correct choices.

No, this is not a correct statement.
In a histogram, horizontal axis represents the class intervals whose width is fixed & the varying data is plotted along the y-axis. So in all  the rectangles of a histogram, width remains same & the length changes.
So correct statement is "In a histogram, the area of each rectangle is proportional to the frequency of its class."

Histograms are a special form of bar chart where the data represents continuously rather than discrete categories. This means that in a histogram there are no gaps between the columns representing the different categories.

It is fundamental concept that histogram is used to obtain mode from continuous frequency distribution graphically.

From the question we are going to form frequency table :