The mean and standard deviation of marks obtained by 50 students of a class in three subjects, Mathematics, Physics and Chemistry are given below:
Subject Mathematics Physics Chemistry Mean 42 32 40.9 Standard deviation 12 15 20
Which of the three subjects shows the highest variability in marks and which shows the lowest?
The mean and standard deviation of marks obtained by 50 students of a class in three subjects, Mathematics, Physics and Chemistry are given below:
| Subject | Mathematics | Physics | Chemistry |
| Mean | 42 | 32 | 40.9 |
| Standard deviation | 12 | 15 | 20 |
Which of the three subjects shows the highest variability in marks and which shows the lowest?
Solution and Explanation
Standard deviation of Mathematics = 12
Standard deviation of Physics =15
Standard deviation of Chemistry = 20
The coefficient of variation (C.V.) is given by \(\frac{Standard\,deviation}{Mean}×100\)
\(C.V(in\,Mathematics)=\frac{12}{42}×100=28.57\)
\(C.V(in\,Physics)=\frac{15}{32}×100=46.87\)
\(C.V(in\,Chemistry)=\frac{20}{40.9}×100=48.89\)
The subject with greater C.V. is more variable than others.
Therefore, the highest variability in marks is in Chemistry and the lowest variability in marks is in Mathematics.
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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.