Revision: Statistics >> Graphical Representation of Statistical Data Maths (English Medium) ICSE Class 10 CISCE

Frequency:

The number of times a particular observation occurs.

Frequency Distribution:

A tabular arrangement of data showing the frequency of each observation or class.

The difference between the highest and lowest observations.

Range = Highest value − Lowest value

• Inclusive form: Both lower and upper limits are included in the class.
  (Example: 1–10, 11–20)

• Exclusive form: Lower limit is included, but upper limit is excluded.
  (Example: 0–10, 10–20)

Statistics is the area of study dealing with the collection, presentation, and analysis of data as well as drawing meaningful conclusions from the data.

A collection of given facts or figures, usually expressed in numerical form.

Each group into which raw data is divided is called a class interval.

The two values that bound a class interval.

• Lower limit: Smallest value of the class

• Upper limit: Largest value of the class

The cumulative frequency of a class interval is the sum of the frequencies of all the classes up to this class interval.

An ogive is a freehand curve obtained by plotting upper class limits on the x-axis and their corresponding cumulative frequencies on the y-axis.

\[\text{Adjustment Factor}=\frac{1}{2}\text{(Lower limit of next class - Upper limit of previous class)}\]

\[\text{Frequency density}=\frac{\mathrm{Frequency}}{\text{Class width}}\]

• A Histogram is a graphical representation of a grouped frequency distribution using rectangles.

• It is used for continuous grouped data.

• Class intervals are shown on the X-axis.

• Frequencies are shown on the Y-axis.

• Rectangles are drawn without gaps between them.

• The height of each rectangle is proportional to its frequency.

• A frequency polygon is a graph obtained by joining the points
  (class-mark, frequency) by straight line segments.

• Class-mark = midpoint of the class interval.

• Two imagined classes (with zero frequency) are taken at the beginning and end to close the polygon.

• A frequency polygon is drawn on the same axes as the histogram (if a histogram is given).

• The polygon starts and ends on the x-axis.

• Ogive is also called a cumulative frequency curve.

• The ogive is also called the less-than ogive.

• It is always a rising curve.

• It starts at the lower limit of the first class with a cumulative frequency of 0.

• It ends at the upper limit of the last class.

• Ogive is drawn only after converting inclusive classes into an exclusive form.