Stats And Maths

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Two variables are associated if variation in one variable has effect on variation in other variables.

It is a measure of association between variables.

Scatter Diagram or Scatter Plot
It is graph obtained by plotting of values of two variables which describe single bivariate observation (e.g. height and weight of a person). One variable (independent variable) X coordinate and the other variable (dependent variable) as Y coordinate.

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Normal Distribution.

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Distribution gives idea about how individuals are distributed in the population. It can be represented by a generalized frequency curve. The distribution can also be represented by some mathematical relationship known as distribution function.

Number of times the experiment is repeated is called as number of trials.

Binomial Distribution.

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Dispersion gives idea of spread of data from the central value say mean.

Deviation is the difference between a observation and some reference value. Observation value is usually represented by X bar.
Deviation of x from some value A is X – A.
Deviation from mean is X – X

Absolute deviation
When deviation is always taken as positive irrespective of its sign, it is called as absolute deviation. It is represented as | X – X |

Mean deviation

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Central Tendency
Central Tendency is the tendency of the data to converge at some value.

Measures of Central Tendency
Measures Central Tendency are the numerical values representative of the data. These are mean, mode and median.

Arithmetic Mean
It is given by sum of all observations divide by total number of observations. Consider the observations 10,15,20,30,35.
Arithmetic mean = [10+15+20+30+35] / 5 = 19

Geometric Mean
It is given by nth root of product of all observations where n is total number of observations . Geometric mean of 2,2,2,8

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Ordinal Variable.
A variable whose possible values can be arranged in some order, such as short, medium, long . In contrast, a variable whose possible values are India, China, USA, are not ordinal variables. Arithmetic with the possible values of an ordinal variable does not necessarily make sense, but it does make sense to say that one possible value is larger than another.

Random Variable.
A random variable denotes possible outcomes of a random experiment.

Random Experiment.

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Variable or Variate.
A letter which can take values of all observations. e.g. If variable x represent marks of three students who have scored 40, 50 and 60 marks, then x1 = 40, x2 = 50, x3 = 60.

Categorical Variable.
A variable whose value ranges over categories, such as male, female. Some categorical variables are ordinal.

Continuous Variable.

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Sampling error:
Sampling errors are the errors in the sample selection which can lead to incorrect results. Sampling errors are broadly classified as random errors, error to due bias or systematic errors.

Random Error.
All measurements are subject to error, which can often be broken down into two components: a bias or systematic error, which affects all measurements the same way; and a random error, which is in general different each time a measurement is made, and behaves like a number drawn with replacement from a box of numbered tickets whose average is zero.

Systematic error.

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Data or Data Set
Data is a set of measurements of some qualitative aspect or quantitative aspect. If we record earnings of five persons in a city, say 100, 200, 200, 500, 1000 (in Rs) then those figures will be our data set or data.

Unit is an individual about which data is to be collected. e.g Person.

Observation is individual measurement in a data set. e.g Rs. 700

Quantitative Data
Quantitative data is data which has numerical value e.g. the above data. Another example is marks obtained by students in a class.

Qualitative Data