Suppose a class has 7 students. The average marks of these students in the mathematics examination is 62, and their variance is 20. A student fails in the examination if he/she gets less than 50 marks, then in worst case, the number of students can fail is __________.
Correct Answer: 0
Solution and Explanation
The correct answer is 0
According to given data
\(\frac{\sum_{i=1}^{7}(x_i - 62)^2}{7} = 20\)
\(\sum_{i=1}^{7} (x_i - 62)^2 = 140\)
So for any xi , (xi – 62)2 ≤ 140
⇒ xi > 50 ∀ i = 1, 2, 3, …7
Therefore, no student is going to score less than 50.
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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.