The range of a set of data is the difference between the highest and lowest values in the set. To find the range, first order the data from least to greatest. Then subtract the smallest value from the largest value in the set.

Mean deviation

The mean deviation is a measure of the dispersion or spread of a set of data values. It measures how far, on average, the data values deviate from their mean or average value. The mean deviation is also known as the average deviation.

Arithmetic mean of deviations

The mean deviation is calculated by finding the arithmetic mean of the absolute deviations of the data values from their mean. The arithmetic mean is simply the sum of all the values divided by the number of values. The absolute deviation is the absolute value of the difference between a data value and the mean.

Explanation of the options

a) Standard deviation: The standard deviation is another measure of the spread of a set of data values. It is calculated by finding the square root of the variance, which is the average of the squared deviations from the mean. The standard deviation provides a more precise measure of dispersion compared to the mean deviation.

b) Mean deviation: The mean deviation, as explained above, measures the average deviation of data values from their mean. It is a simple measure of dispersion but does not take into account the direction of deviations.

c) Quartile deviation: The quartile deviation is a measure of dispersion that uses quartiles, which divide a dataset into four equal parts. It is calculated by finding the difference between the first quartile and the third quartile. The quartile deviation provides information about the spread of data around the median.

d) Range: The range is the simplest measure of dispersion and is calculated by finding the difference between the largest and smallest values in a dataset. It gives an idea of the spread of data but does not consider the individual values or their deviations from the mean.

Conclusion

In summary, the arithmetic mean of the deviations of items from some average value is called the mean deviation. It provides a measure of the average deviation of data values from their mean. The other options, such as standard deviation, quartile deviation, and range, are alternative measures of dispersion that provide additional information about the spread of data values.

B