All the students of a class performed poorly in
Mathematics. The teacher decided to give grace
marks of $10$ to each of the students. Which of the following statistical measures will not change even after the grace marks were given?
- Mean
- Median
- Mode
- Variance
The Correct Option is D
Solution and Explanation
$ \sigma_1^2 = \frac{ \sum \, ( x_i - \overline{ x} )^2 }{ N}$
Now, each is increased by 10
$\therefore \sigma_1^2 = \frac{ \sum [ ( x_i + 10 ) - ( \overline{ x} + 10)]^2 }{ N} = \sigma_1^2 $
So, variance will not change whereas mean, median and
mode will increase by 10.
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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.