LECTURE 5 Flashcards
What is dispersion?
The spread or variation of data points around a central value.
What is the purpose of dispersion?
To measure the variability of data and provide a complete picture beyond averages.
What are the characteristics of a good measure of dispersion?
- Rigidly defined 2. Based on all observations 3. Not affected by extreme values 4. Allows algebraic manipulation 5. Simple to calculate and understand.
What is the range?
The difference between the largest and smallest values in a dataset.
What is the formula for range?
Range = L - S, where L is the largest value and S is the smallest value.
What is the range for continuous data using Method 1?
L = Upper boundary of the highest class, S = Lower boundary of the lowest class.
What is the range for continuous data using Method 2?
L = Midpoint of the highest class, S = Midpoint of the lowest class.
What are the merits of range?
- Simple to calculate 2. Easy to understand 3. Useful in quality control, weather forecasts, and stock analysis.
What are the demerits of range?
- Affected by extreme values 2. Based on only two observations 3. Not suitable for open-end intervals 4. Rarely used as a standalone measure.
What is standard deviation (SD)?
The positive square root of the arithmetic mean of squared deviations from the mean.
What is the formula for standard deviation for raw data?
s = √[Σ(x - x̄)² / n].
What is the formula for standard deviation for grouped data (discrete)?
s = √[Σf(x - x̄)² / n].
What is the formula for standard deviation for grouped data (continuous)?
s = √[Σf(d²) / n - (Σf(d) / n)²], where d = x - A.
What are the merits of standard deviation?
- Rigidly defined 2. Uses all observations 3. Suitable for mathematical analysis 4. Less affected by sampling fluctuations.
What are the demerits of standard deviation?
- Difficult to compute 2. Gives more weight to extreme values 3. Cannot be used for direct comparisons.
What is variance?
The square of the standard deviation.
What is the formula for variance?
Variance = (SD)².
What is the coefficient of variation (CV)?
A relative measure of dispersion expressed as a percentage.
What is the formula for coefficient of variation (CV)?
CV = (SD / Mean) × 100.
What is the purpose of CV?
To compare variability between datasets with different units.
What is an example of using CV for comparison?
If CV for yield is 20% and for plant height is 9.1%, yield is more variable.
Which measure is affected most by extreme values?
Standard Deviation.
Variance is the square of which measure?
Standard Deviation.
If CV of Variety I is 30% and Variety II is 25%, which is more consistent?
Variety II.
For the dataset 5, 5, 5, 5, 5, 5, what is the standard deviation?
0
Do absolute measures of dispersion have the original units?
Yes.
Can the mean deviation value for a dataset be negative?
No.
Define dispersion.
The spread or variation of observations from their central value.
Define CV and its uses.
CV is the ratio of SD to the mean expressed as a percentage. It compares variability between datasets with different units.
What are the differences between absolute and relative measures of dispersion?
- Absolute measures have the same units as the data (e.g., Range, SD). 2. Relative measures (e.g., CV) are unitless and expressed in percentages.
How is standard deviation calculated for raw data?
Using the formula: s = √[Σ(x - x̄)² / n].
How is standard deviation calculated for grouped data?
Using the formula: s = √[Σf(d²) / n - (Σf(d) / n)²], where d = x - A.
