Measures of Dispersion:

Measures of dispersion are used to describe how spread out a set of data is. They provide information about the variability or diversity of the data. Some common measures of dispersion are:

1. Mean deviation
2. Standard deviation
3. Quartile deviation

Which measure of dispersion is based on all the observations?

The correct answer is (D) Mean deviation and Standard deviation but not Quartile deviation.

Explanation:

1. Mean deviation:

Mean deviation is a measure of dispersion that is based on all the observations in a data set. It measures the average distance between each data point and the mean of the data set. It is calculated by taking the sum of the absolute differences between each data point and the mean of the data set, and then dividing by the number of observations.

2. Standard deviation:

Standard deviation is another measure of dispersion that is based on all the observations in a data set. It measures the amount of variation or spread in a data set. It is calculated by taking the square root of the variance, which is the average of the squared differences between each data point and the mean of the data set.

3. Quartile deviation:

Quartile deviation is a measure of dispersion that is based on the middle 50% of the observations in a data set. It measures the spread of the data around the median. It is calculated by taking the difference between the upper and lower quartiles.

Conclusion:

Mean deviation and Standard deviation are based on all the observations in a data set, whereas Quartile deviation is based on only the middle 50% of the observations. Therefore, the correct answer is (D) Mean deviation and Standard deviation but not Quartile deviation.

For calculating mean deviation, we calculate mean first and for mean we consider all the observations.
For S.D, we calculate mean first so it is also based on all observations.
But for Q.D we calculate no of observations in raw data and for classes we take limits.