Coefficient of Variation Calculation

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Questions and Answers

What is the formula to calculate the relative mean deviation?

Sum of deviations divided by the number of items

Average divided by the mean deviation

Mean deviation divided by the average (correct)

Total frequency divided by the total deviation

How is the coefficient of mean deviation calculated?

Dividing total deviations by the number of items (correct)

Dividing total frequency by the total deviation

Dividing total deviations by the average

Dividing mean deviation by the average

For grouped data in a discrete series, what is used to represent the deviations from the average?

|P|

|N|

|f|

|D| (correct)

In discrete series for grouped data, what does 'P' represent in the formula for mean deviation?

|f| Signup and view all the answers

What is the process to find standard deviation for a continuous series?

Calculate f |D| and divide by N Signup and view all the answers

Which measure is calculated using deviations from the average ignoring signs?

Mean deviation Signup and view all the answers

What is the correct formula to calculate Standard Deviation for Grouped data - Continuous Series?

σ = √(Σ(fd^2)/(N)) Signup and view all the answers

In the context of calculating Standard Deviation for Grouped data - Discrete Series, what does 'd' represent in the formula?

Difference between each value and the assumed value Signup and view all the answers

For the provided data, what is the calculated Standard Deviation?

16.8 Signup and view all the answers

What is a common use of the Coefficient of Variation (C.V.) in statistics?

To measure the spread of a distribution Signup and view all the answers

When comparing two sets of data using the Coefficient of Variation (C.V.), what does a higher C.V. indicate?

Higher relative variability Signup and view all the answers

What can be inferred about the stability of prices in City A compared to City B based on the given price data?

City A has more stable prices Signup and view all the answers

What is the purpose of converting standard deviation into the coefficient of variation?

To compare the variability of two or more series Signup and view all the answers

For grouped data in a discrete series, how is standard deviation calculated?

$σ = \sqrt{\frac{∑fd^2}{N}}$ Signup and view all the answers

Which scenario does a greater coefficient of variation indicate?

More variability and less consistency Signup and view all the answers

In grouped data for a continuous series, what does 'd' represent in the standard deviation formula?

Difference between x and A Signup and view all the answers

What does a smaller coefficient of variation imply about a group of data?

More homogeneity and uniformity Signup and view all the answers

When comparing two groups of data, if one group has a higher C.V. than the other, what does this suggest?

The group with higher C.V. is more variable Signup and view all the answers

Study Notes

Relative Mean Deviation and Coefficient of Mean Deviation

The formula for calculating the Relative Mean Deviation is the Mean Deviation (MD) divided by the Mean (M), often expressed as ( RMD = \frac{MD}{M} ).
The Coefficient of Mean Deviation is computed as the Mean Deviation divided by the Average, providing a measure of relative variability.

Deviations in Grouped Data

For grouped data in a discrete series, deviations from the average are represented using mid-point values corresponding to each class interval.
In discrete series for grouped data, 'P' represents the frequency of a particular class interval in the formula for calculating Mean Deviation.

Standard Deviation Calculation

To find Standard Deviation for a continuous series, the process involves calculating the mean, determining deviations from the mean, squaring those deviations, and obtaining the average of the squared deviations before taking the square root.
A measure like Mean Deviation is calculated using deviations from the average while ignoring the signs, hence focusing on absolute values.

Formulas for Standard Deviation

The correct formula for Standard Deviation in Grouped Data (Continuous Series) is expressed as ( SD = \sqrt{\frac{\sum f (x - \bar{x})^2}{N}} ), where ( f ) is the frequency, ( x ) is the mid-value, and ( \bar{x} ) is the mean.
In the context of calculating Standard Deviation for Grouped Data (Discrete Series), 'd' denotes the deviation of each class midpoint from the overall mean.

Coefficient of Variation (C.V.)

The Coefficient of Variation (C.V.) is commonly used to compare the relative variability of two or more data sets, allowing for comparisons even on different scales.
A higher Coefficient of Variation indicates greater variability relative to the mean in the dataset being analyzed.

Price Stability Comparison

Comparing price stability, if City A has a lower C.V. than City B, it suggests that prices in City A are more stable.
The purpose of converting standard deviation into the Coefficient of Variation is to standardize dispersion across datasets with different units or means.

Standard Deviation Calculation for Grouped Data

For grouped data in a discrete series, standard deviation is calculated by finding the mean of the data, determining frequency multiplied by the squared deviations, and then applying the appropriate formula for variance and standard deviation.
A greater Coefficient of Variation indicates a higher level of relative variability within the dataset, suggesting less consistency.

Implications of Coefficient of Variation

A smaller Coefficient of Variation implies greater precision and lesser variability in the data set, indicating a more consistent group of data.
When comparing two groups of data, a higher C.V. in one group suggests that it has greater variability compared to the other group.

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Description

Learn how to calculate the coefficient of variation to compare the relative dispersion of data sets with different units, such as heights in centimeters and weights in kilograms. Understand the formula and its application in statistics.