The variance of 50 observations is 7. Suppose that each observation in this data is multiplied by 6 and then 5 is subtracted from it. Then the variance of that new data is
The variance of 50 observations is 7. Suppose that each observation in this data is multiplied by 6 and then 5 is subtracted from it. Then the variance of that new data is
37
42
247
252
The Correct Option is D
Solution and Explanation
To solve this problem, let's first understand the impact of the given transformations on variance. The initial variance of 50 observations is given to be 7.
- When every observation in a dataset is multiplied by a constant \(c\), the variance becomes \(c^2\) times the original variance. If the original variance is \(\sigma^2\), then the new variance is \(c^2 \sigma^2\).
- Subtracting a constant from each observation does not affect variance, so it can be ignored.
Given that each observation is multiplied by 6 (and then 5 is subtracted), only multiplication affects variance.
Original variance:
\[ \sigma^2 = 7 \]New variance after multiplication by 6:
\[ \text{New variance} = 6^2 \times 7 = 36 \times 7 \] \[ = 252 \]Therefore, the variance of the new data is:
252
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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.