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?,
- Which of the following is the first step in calculating the median of data set?
1. Average the middle two values of the data set
2. Array the data
3. Determine the relative weights of the data values in terms of importance
4. Find the average distance of the observations in the data set from the mean - If the median of a data is 61.54 less than its mode, then the median of the data exceeds its mean by _____. (Use the empirical formula to find the answer)
The mean marks of the following distribution is:
Marks Obtained No. of Students 81 15 35 4 73 3 56 16 - The sum of deviations of the items from __________ ignoring signs is the least?
