Question:

Fill in the blanks. (i) The standard deviation of a data is of any change in origin, Put is on the change of scale. (ii) The sum of squares of the deviations of the values of the variable is when taken about their arithmetic mean. (iii) The mean deviation of the data is when measured from the median. (iv) The standard deviation is to the mean deviation taken from the arithmetic mean.

Updated On: Jul 6, 2022
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  • b
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The Correct Option is A

Solution and Explanation

(i) The standard deviation of a data is independent of any change in origin, but is dependent on change of scale. (ii) The sum of the squares of the deviations of the values of the variable is minimum when taken about their arithmetic mean. (iii) The mean deviation of the data is least when measured from the median. (iv) The $S.D.$ is greater than or equal to the mean deviation taken from the arithmetic mean.
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Notes on Statistics

Concepts Used:

Statistics

Statistics is a field of mathematics concerned with the study of data collection, data analysis, data interpretation, data presentation, and data organization. Statistics is mainly used to acquire a better understanding of data and to focus on specific applications. Also, Statistics is the process of gathering, assessing, and summarising data in a mathematical form.

Mathematically there are two approaches for analyzing data in statistics that are widely used:

Descriptive Statistics -

Using measures of central tendency and measures of dispersion, the descriptive technique of statistics is utilized to describe the data collected and summarise the data and its attributes.

Inferential Statistics -

This statistical strategy is utilized to produce conclusions from data. Inferential statistics rely on statistical tests on samples to make inferences, and it does so by discovering variations between the two groups. The p-value is calculated and differentiated to the probability of chance() = 0.05. If the p-value is less than or equivalent to, the p-value is considered statistically significant.