Calculating Mode using Empirical Relation
The problem asks for the mode of a data set given its mean and median.
Given Data:
- Mean ($ \bar{x} $) = 20
- Median (M) = 30
Empirical Relation:
For a moderately skewed distribution, the empirical relationship between mean, median, and mode is given by:
Mode $ = 3 \times \text{Median} - 2 \times \text{Mean} $
Or, using notation:
Mode $ = 3M - 2\bar{x} $
Calculation:
Substitute the given values into the formula:
Mode $ = (3 \times 30) - (2 \times 20) $
Mode $ = 90 - 40 $
Mode $ = 50 $
Result:
The mode of the data is 50.
Important Questions from Elementary Statistics
Demand for seats in a university is at its highest in the fall; demand also trends to grow and fall off in 25 year waves. In time service forecasting, the former demand characteristic would be called ______ and the latter would be called _______.
The system of combining two or more overlapping series of index numbers to obtain a single continuous series is called
The rise in the number of patients due to heatstroke is an example of:
According to government data, 24 percent of teenagers in India under the age of 18 years live in households with incomes that are classified at a particular income level. A simple random sample of 400 teenagers in India under the age of 18 years was selected for a study of learning. If the government data is correct, which of the following best approximates the probability that at least 27 per cent of the teenagers in the sample live in households that are classified at a particular income level?
Which index satisfies the factor reversal test?
