Geometric Mean Calculation: Observations Multiplied by Constant
This problem involves finding the new geometric mean (GM) after each observation in a dataset is multiplied by a constant factor.
Key Property of Geometric Mean
If the geometric mean of $n$ observations $x_1, x_2, ..., x_n$ is $G$, and each observation is multiplied by a constant $c$, the new geometric mean $G_{new}$ is given by:
$ G_{new} = c \times G $
Problem Breakdown
Given:
- Number of observations, $n = 100$
- Original Geometric Mean, $G = 25$
- Constant multiplier, $c = 4$
Calculating the New Geometric Mean
Using the property stated above, we can calculate the new geometric mean:
- Identify the original GM: $G = 25$.
- Identify the multiplier: $c = 4$.
- Apply the formula: $G_{new} = c \times G$.
- Substitute the values: $G_{new} = 4 \times 25$.
- Calculate the result: $G_{new} = 100$.
Therefore, the new geometric mean is 100.
Important Questions from Elementary Statistics (Notes)
Let $X_1, X_2, X_3$ be a random sample of size 3 from an absolutely continuous distribution that is symmetric about 0. For $i=1,2,3$, let $R_i$ denote the rank of $|X_i|$ among $|X_1|, |X_2|$ and $|X_3|$.
If $T^+ = \sum_{i=1, X_i>0}^3 R_i$
is the Willcoxon signed-rank statistic, then which of the following statements are true?,
- What is the geometric mean of 2, 4 and 8?
- In correlation analysis, the two variables
1. Are treated with distinction.
2. Are treated differently based on individual characteristics.
3. Are treated symmetrically.
4. Are regressed. - In statistics, standard error measures the
1. Specification error of the model.
2. Autocorrelation in the regression model.
3. Correlation between dependent and independent variables.
4. Precision of an estimate. - Linear regression model is
1. linear in explanatory variables but may not be linear in parameters
2. non-linear in parameters and must be linear in variables
3. linear in parameters and must be linear in variables
4. linear in parameters and may be linear in variables
