Question

What is mean, mode, standard deviation, and error?

Answer 1

solution:

a) Mean : For a data set Arithemetic Mean is the central value a discrete set of numbers .The mean (average) of a data set is found by adding all the numbers in a data set and then dividing by the no.of values in the data set.

It is also called as 'Expected value' or 'Average'.

Ex: A data set consists of 5 numbers : 1,2,3,4,5 ,Then it's Mean = (1+2+3+4+5)/5 = 3

--->The mean can be used for both 'Continuous and discrete 'numeric' data.

---> The mean cannot be calculated for the categorical data as the vales cannot be summed

--->As the mean includes every value from the distribution ,it is influenced by outliers and skewed distributions

1) Mean for ungrouped data:

Mean =

2) Mean for grouped data

Mean () =

b) Mode:Mode is the most frequently occured value in a distribution.

Ex: The mode of data set : 1,1,2,3,3,3,3,4,5 is 3

---> It has an advantage over mean and median as it can be calculated for both numerical and categorical data

---> Mode always may not reflect the 'centre of the distribution'

---> A data set have more than 1 mode.

If a data set has 1 mode - uni modal data

. If a data set have2 modes - Bi modal data

   If a data set have more than 2 modes - Multi-Modal data

1) Mode for grouped data

Mode = L + [ (f1-f0) / (2f1-f0-f2) ] * h

where L = lower limit of modal class

h = size of modal class

f0 = frequency of class preceeding the modal class

f1 = frequency of the modal class

f2 = frequency of class succeeding the modal class

c) Standard deviation: It is the measure of amount of variation (or) dispersion of a set of values.

----> If a data set have low standard deviation then the values tends to close to mean

----> If a data set have high standard deviation then the values are spread out over a wider range.

--->As the standard deviation includes every value from the distribution ,it is influenced by outliers and skewed distributions

1) Standard deviation for ungrouped data

2) Standard deviation for grouped data

[ Note: Sample standard deviation is the standard deviations of randomly selected samples from a population.it is represented by (s). But In formula  denominator is N-1 ]

d) Error: Error is the difference between a value obtained from a data collection process and true value for the population.The greater the error ,the less the representative of the data of the population .

Data can be highly effected by two types of errors

• Sampling Error: It occurs as a result of using a sample from the population rather than conducting the complete enumeration of the population.It refers to the difference between an estimate for a population based on data and 'true' values of the population
• Non-sampling Error: It is caused by factors other than those related to sampling selection.Due to the presence of factors ,whether systemic or random that results in the data values are not accurately reflecting the true value of the population.