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)
- 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 - The sum of deviations of the items from __________ ignoring signs is the least?
- The relationship between mean, median and mode is:
Which of the following statements are correct?
(A).When a cyclical pattern in data has a period of less than 1 year, the pattern in data is called seasonal variation
(B). When a cyclical pattern has a period more than 1 year, we refer to it as cyclical variation
(C). Seasonality is considered equivalent to forecasting
(D). Cyclical behaviour in business is also termed as business cycle
Choose the correct answer from the options given below:Match List-I with List-II
List-1 List-II Methods to Deseasonalise the Time Series Underlying Meaning (A). Method of simple average (I). It assumes that seasonal variation for a given month is constant fraction of trend (B). Ratio to Trend Method (II). It is the easiest method of obtaining a seasonal index (C). Ratio to moving average method (III). It is the most difficult method of measuring seasonal variations (D). Link relative method (IV). It is also known as the percentage of moving average method
Choose the correct answer from the options given below:
