Question

Which of the following ratios is true about standard deviation, mean deviation, and quartile deviation:

Options:
a. (i) 10:12:15
b. (ii) 15:12:10
c. (iii) 15:10:12
d. (iv) 6:5:4

Answer 1

The correct ratio about standard deviation, mean deviation, and quartile deviation is option (ii) 15:12:10.

Step-by-step explanation:

The correct ratio about standard deviation, mean deviation, and quartile deviation is option (ii) 15:12:10.

To understand this, let's define each term:

• Standard Deviation: It measures the amount of variation or dispersion in a set of values. A higher standard deviation indicates greater variability in the data.
• Mean Deviation: It measures the average distance of each data point from the mean. It is calculated by summing the absolute differences between each data point and the mean, and then dividing by the number of data points.
• Quartile Deviation: It measures the spread of the middle 50% of the data. It is the difference between the third quartile (Q3) and the first quartile (Q1).

In option (ii) 15:12:10, the standard deviation is 15, which is the largest value, indicating the greatest variability. The mean deviation is 12, and the quartile deviation is 10. Therefore, option (ii) is the correct ratio.