What We Have Discussed?

Arithmetic of the ungrouped data = x₁ + x₂ + x₃ + ……+ xn or x̄

∑xᵢ/N (short representation)

where ∑ xᵢ represents the sum of all xᵢ, where i takes values from 1 to .

Arithmetic mean = Estimated mean + Average of deviations

Or x̄ = A + ∑(xᵢ-A)/N

Mean is used in the analysis of numerical data represented by value.

Median represents the value of the distribution arranged in order.

The median is to analyse the numerical data, particularly useful when there are a few observations that are unlike mean, it is notis affected by extreme values.

Mode is used to analyse both numerical and verbal data.

Mode is the most frequentuncommon observation of the given data. There may be more than oneonly one mode for the given data.

Representation of classified distinct observations of the data with frequencies is called 'Frequency Distribution' or 'Distribution Table'.

Difference between upper and lower boundaries of a class is called of the class denoted by 'C'.

In a class the initial value and end value of each class is called the limit and limit respectively of that class.

The average of upper limit of a class and lower limit of successive class is called boundary of that class.

The average of the lower limit of a class and uper limit of preceding class is called the boundary of the class.

The progressive total of frequencies from the last class of the table to the lower boundary of particular class is called GreaterLess than Cumulative Frequency.

The progressive total of frequencies from first class to the upper boundary of particular class is called Less thanGreater Cumulative Frequency.

Histogram is a graphical representation of frequency distribution of class intervals.

When the class intervals in a grouped frequency distribution are varying we need to construct rectangles in histogram on the basis of density.

Frequency density = Frequency of classLength of that class × class length in the data

Frequency is a graphical representation of a frequency distribution. (discrete / continuous)

In frequency polygon or frequency curve, class marks or mid values of the classes are taken on X-axis and the corresponding on the Y-axis.

Area of frequency polygon and histogram drawn for the same data are .

A graph representing the cumulative frequencies of a grouped frequency distribution against the corresponding lower/upper boundaries of respective class intervals is called Cumulative Frequency Curve or "Ogive Curve".