Page 1
STATISTICS
Stastics is a branch of mathematics which deals with collection, grouping, analysis of the data and then
to derive the results which are representative of the data collected. Single value of the variable describing
the data is called an average. Average lies on generally in the middle of data so such values are called
measures of central tendency. Common measures are mean, median and mode.
Page 2
STATISTICS
Stastics is a branch of mathematics which deals with collection, grouping, analysis of the data and then
to derive the results which are representative of the data collected. Single value of the variable describing
the data is called an average. Average lies on generally in the middle of data so such values are called
measures of central tendency. Common measures are mean, median and mode.
Mean, Median and Mode
The degree to which the values in a set of data are spread around an average is called dispersion of
variation. The different measures of dispersion are range, quartile deviation, mean deviation, standard
deviation and variance. Statistics finds a wide application in finance, economics, various surveys,
planning, demography and various other analysis. All future planning of a country depends upon
statistics of growth or fall in population, industrial production, crop production etc.
Page 3
STATISTICS
Stastics is a branch of mathematics which deals with collection, grouping, analysis of the data and then
to derive the results which are representative of the data collected. Single value of the variable describing
the data is called an average. Average lies on generally in the middle of data so such values are called
measures of central tendency. Common measures are mean, median and mode.
Mean, Median and Mode
The degree to which the values in a set of data are spread around an average is called dispersion of
variation. The different measures of dispersion are range, quartile deviation, mean deviation, standard
deviation and variance. Statistics finds a wide application in finance, economics, various surveys,
planning, demography and various other analysis. All future planning of a country depends upon
statistics of growth or fall in population, industrial production, crop production etc.
Mean
Also called arithmetic mean or simply average.
Unclassified data: The mean of ?? observations ?? 1
, ?? 2
, … ?? ?? is defined as
?? ? =
?? 1
+ ?? 2
+ ?? 3
+ ? + ?? ?? ?? =
1
?? ? ?
?? ?? =1
?? ??
Page 4
STATISTICS
Stastics is a branch of mathematics which deals with collection, grouping, analysis of the data and then
to derive the results which are representative of the data collected. Single value of the variable describing
the data is called an average. Average lies on generally in the middle of data so such values are called
measures of central tendency. Common measures are mean, median and mode.
Mean, Median and Mode
The degree to which the values in a set of data are spread around an average is called dispersion of
variation. The different measures of dispersion are range, quartile deviation, mean deviation, standard
deviation and variance. Statistics finds a wide application in finance, economics, various surveys,
planning, demography and various other analysis. All future planning of a country depends upon
statistics of growth or fall in population, industrial production, crop production etc.
Mean
Also called arithmetic mean or simply average.
Unclassified data: The mean of ?? observations ?? 1
, ?? 2
, … ?? ?? is defined as
?? ? =
?? 1
+ ?? 2
+ ?? 3
+ ? + ?? ?? ?? =
1
?? ? ?
?? ?? =1
?? ??
Mean
Grouped data: Let ?? 1
, ?? 2
, … ?? ?? be ?? observation with corresponding frequencies as ?? 1
, ?? 2
, ?? 3
, … ?? ??
respectively, then
?? ? =
?? 1
?? 1
+ ?? 2
?? 2
+ ?? 3
?? 3
+ ? + ?? ?? ?? ?? ?? 1
+ ?? 2
+ ? + ?? ?? =
? ?
?? ?? =1
??? ?? ?? ?? ? ?
?? ?? =1
??? ??
Page 5
STATISTICS
Stastics is a branch of mathematics which deals with collection, grouping, analysis of the data and then
to derive the results which are representative of the data collected. Single value of the variable describing
the data is called an average. Average lies on generally in the middle of data so such values are called
measures of central tendency. Common measures are mean, median and mode.
Mean, Median and Mode
The degree to which the values in a set of data are spread around an average is called dispersion of
variation. The different measures of dispersion are range, quartile deviation, mean deviation, standard
deviation and variance. Statistics finds a wide application in finance, economics, various surveys,
planning, demography and various other analysis. All future planning of a country depends upon
statistics of growth or fall in population, industrial production, crop production etc.
Mean
Also called arithmetic mean or simply average.
Unclassified data: The mean of ?? observations ?? 1
, ?? 2
, … ?? ?? is defined as
?? ? =
?? 1
+ ?? 2
+ ?? 3
+ ? + ?? ?? ?? =
1
?? ? ?
?? ?? =1
?? ??
Mean
Grouped data: Let ?? 1
, ?? 2
, … ?? ?? be ?? observation with corresponding frequencies as ?? 1
, ?? 2
, ?? 3
, … ?? ??
respectively, then
?? ? =
?? 1
?? 1
+ ?? 2
?? 2
+ ?? 3
?? 3
+ ? + ?? ?? ?? ?? ?? 1
+ ?? 2
+ ? + ?? ?? =
? ?
?? ?? =1
??? ?? ?? ?? ? ?
?? ?? =1
??? ??
Mean
Shortcut method : Let the assumed mean (usually the middle term of the data) be ?? .
The deviation from assumed mean, ?? ?? = ( ?? ?? - ?? ) for each term
?? ? = ?? +
? ?? ?? ?? ?? ? ?? ??
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