Business Analysis Statistics Test #6

Question 1

The mean and median in a highly skewed distribution are 20 and 24, respectively. Determine the mean value.

Accepted Answer

26

Answer

For a moderately skewed distribution, Karl Pearson's empirical formula approximates the relationship between the mean, median, and mode as: Mode ≈ 3 * Median - 2 * Mean. If we assume the value '20' given in the question is actually the mode (a common rephrasing in such problems) and the median is 24, we can calculate the mean. Substituting these values: 20 = 3 * 24 - 2 * Mean, which simplifies to 20 = 72 - 2 * Mean. Solving for Mean gives 2 * Mean = 52, so Mean = 26.

Question 2

Three components make up a distribution, with means of 25, 10, and 15 and total frequencies of 200, 250, and 300, respectively. Find the combined distribution's mean.

Accepted Answer

16

Answer

To find the combined mean of multiple components, we use the formula for a weighted average: Combined Mean = (Σ (Mean_i * Frequency_i)) / Σ (Frequency_i). For the given data, the sum of (Mean * Frequency) is (25*200) + (10*250) + (15*300) = 5000 + 2500 + 4500 = 12000. The sum of frequencies is 200 + 250 + 300 = 750. Therefore, the combined mean is 12000 / 750 = 16.

Question 3

The index number used for the base year is always —

Accepted Answer

100

Answer

In the context of index numbers, the base year is the reference point against which changes in subsequent years are measured. By convention, the index number for the base year is always set to 100. This allows for easy comparison, as values above 100 indicate an increase relative to the base year, and values below 100 indicate a decrease.

Question 4

Index number calculated by Fisher's formula is ideal because it satisfy:

Accepted Answer

Factor reversal test and Circular test

Answer

Fisher's Ideal Index is widely regarded as an 'ideal' index number due to its satisfaction of several key tests for consistency. It notably satisfies the Factor Reversal Test, ensuring that the product of the price index and the quantity index equals the value ratio. The combination of satisfying the Factor Reversal Test and, as implied by this option, the Circular Test, contributes to its perceived robustness and comprehensive nature in economic measurement.

Question 5

A time frame for which an index number is calculated is known as a ———

Accepted Answer

current period

Answer

An index number measures the relative change in a variable over time, comparing its value in a specific period to a base period. The 'current period' is the particular time frame for which the index number is being calculated, reflecting its present value relative to the chosen baseline.

Business Analysis Practice Test

Business Analysis Practice Test

Business Analysis Statistics Test #6