What is the formula for calculating the geometric mean (G.M.) of n positive values?

Fill in the blank: The harmonic mean (H.M.) for n observations is calculated as the total number divided by the sum of the ___.

Reciprocals of the numbers.

True or False: The harmonic mean is particularly useful for averaging speeds when distances are equal.

True. The harmonic mean is applicable when calculating average rates, especially in situations involving equal distances.

Define the median and describe its significance in a data set.

The median divides a data set.

• Middle value in order.

• Robust against outliers.

• Reflects central tendency.

What steps are involved in calculating the median for a continuous frequency distribution?

Steps to Calculate Median

• Identify median class using N/2.

• Use median formula for calculation.

• Consider frequency and class boundaries.

How do you compute the K-th percentile of a data set?

Calculate K-th percentile position.

• Position is L = (K/100) * N.

• Average values if L is whole.

• Round L up to find value.

True or False: The mode is always unique in a data set.

False. A data set can have multiple modes (bimodal or multimodal) if two or more values occur with the same maximum frequency.

Fill in the blank: The weighted average method considers both the ___ and ___ of the materials in stock.

Rates and quantities.

What are the disadvantages of using the harmonic mean?

Disadvantages of Harmonic Mean

• Difficult to calculate accurately.

• Not valid for zero or negative.

• May misrepresent mixed data sets.

In the context of averages, what is the significance of quartiles?

Quartiles show data distribution clearly.

• Divide data into four parts.

• Indicate data spread and trends.

• Useful for identifying outliers.