Frequency polygons - class-XII

There are following characteristics of $frequency curve$

Frequency polygon is not a characteristics of frequency curve.
Because frequency polygon is one kind of curve not a characteristics of frequency curve.

A frequency polygon is constructed by joining the midpoints of the tops of histogram bars, while a frequency curve is a smoothed version of a frequency polygon. They are distinct concepts in statistics.

A histogram uses bars to represent frequencies of continuous data, whereas a frequency polygon uses lines connecting points. They are different graphical representations.

A frequency polygon is a line graph used to represent the frequency distribution of a dataset, typically by plotting frequencies against class midpoints.

Frequency curves can take various shapes based on the distribution of data, including symmetrical (normal), positively skewed, or negatively skewed distributions.

An Ogive is specifically defined as the graph of a cumulative frequency distribution.

This is identical to question 394724. An ogive is the curve obtained by plotting cumulative frequencies against class boundaries. The statement 'A curve obtained by plotting cumulative frequencies is called an Ogive' is the standard definition in statistics.

Histograms use rectangular bars to show frequency, while frequency polygons use line segments connecting points. They are fundamentally different in visual representation.

Ogives can be constructed for both 'less than' cumulative frequency distributions and 'more than' cumulative frequency distributions.

Ogives are useful tools in statistics to estimate positional measures such as the median, quartiles, and other percentiles.

The point where the 'less than' ogive and 'more than' ogive intersect on the horizontal axis corresponds to the median of the data distribution.

Plotting cumulative frequencies results in an S-shaped curve known as an Ogive.

An Ogive curve requires cumulative frequencies because it plots the total frequency up to a certain point against the class boundaries.

An ogive plots cumulative frequencies against class boundaries (upper limits), not values with frequencies or frequencies with cumulative frequencies. The correct plotting involves class boundaries vs cumulative frequencies.

A frequency polygon is constructed by plotting the midpoints of class intervals against their respective frequencies and connecting these points with straight line segments. This distinguishes it from a frequency curve, which is typically a smooth line.

Solution:

$\Rightarrow$  The frequency distribution table are as follows :

Curve formed by joining the midpoint of rectangular of histogram is called as frequency curve.

An ogive, also known as a cumulative frequency polygon, is a graphical representation of the cumulative frequency distribution. It is plotted by using the upper boundaries of class intervals on the x-axis and cumulative frequencies on the y-axis.

A histogram consists of adjacent vertical rectangles where the area of each rectangle is proportional to the frequency of the class interval it represents.

By definition, a frequency polygon is constructed by connecting the midpoints of class intervals with straight line segments, forming a polygon shape.

We draw the class marks on the abscissae, class marks are the mean of lower and upper limit of the class intervals.