Solution:

Given, the sum of squares of deviation from mean of 10 observations is 250.

Let's assume the 10 observations as x1, x2, x3, ..., x10.

Also, it is given that the mean of the data is 10.

Therefore, the sum of the observations can be calculated as follows:

Sum of observations = Mean x Number of observations
= 10 x 10
= 100

Calculation of variance:

Variance (s^2) = Sum of squares of deviation from mean / Number of observations
= 250 / 10
= 25

Calculation of standard deviation:

Standard deviation (s) = Square root of variance
= Square root of 25
= 5

Calculation of coefficient of variation:

Coefficient of variation = (Standard deviation / Mean) x 100%
= (5 / 10) x 100%
= 50%

Therefore, the coefficient of variation for the given data is 50%.

Explanation:

The coefficient of variation is a statistical measure that represents the relative variability of a dataset. It is used to compare the variability between two or more datasets of different sizes and means.

In this problem, we are given the sum of squares of deviation from mean of 10 observations and the mean of the data. Using this information, we can calculate the variance and standard deviation of the dataset.

The variance represents the average of squared deviations from the mean, while the standard deviation is the square root of the variance.

Finally, the coefficient of variation is calculated by dividing the standard deviation by the mean and multiplying the result by 100%. This measure provides a relative measure of the amount of variation in the dataset and is commonly used in fields such as finance and economics.