DIGITAL ASSIGNMENT 1 MAT, Assignments of Statistics

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DIGITAL ASSIGNMENT 1

MAT 2001

NAME-SAMBUDDHA CHAKRABORTY

REG.NO- 19 MIS 0007

TITLE

Generally, the central tendency of a dataset can be described using the following

measures:

Mean (Average): Represents the sum of all values in a dataset divided by the total

number of the values.

Median: The middle value in a dataset that is arranged in ascending order (from

the smallest value to the largest value). If a dataset contains an even number of

values, the median of the dataset is the mean of the two middle values.

Mode: Defines the most frequently occurring value in a dataset. In some cases, a

dataset may contain multiple modes while some datasets may not have any mode

at all.

RANGE

The range is the difference between the largest and the smallest observation in the

data. The prime advantage of this measure of dispersion is that it is easy to

calculate. On the other hand, it has lot of disadvantages. It is very sensitive to

outliers and does not use all the observations in a data set.[ 1 ] It is more

informative to provide the minimum and the maximum values rather than

providing the range.

INTERQUARTILE RANGE Interquartile range is defined as the difference between the 25 th and 75 th percentile (also called the first and third quartile). Hence the interquartile range describes the middle 50 % of observations. If the interquartile range is large it means that the middle 50 % of observations are spaced wide apart. The important advantage of interquartile range is that it can be used as a measure of variability if the extreme values are not being recorded exactly (as in case of open- ended class intervals in the frequency distribution).Other advantageous feature is that it is not affected by extreme values. The main disadvantage in using interquartile range as a measure of dispersion is that it is not amenable to mathematical manipulation. STANDARD DEVIATION Standard deviation (SD) is the most commonly used measure of dispersion. It is a measure of spread of data about the mean. SD is the square root of sum of squared deviation from the mean divided by the number of observations.