Final answer:
To find the quartile deviation and its coefficient, arrange the data in order, calculate Q1 and Q3, find the quartile deviation (Q3-Q1)/2, and divide by the average of Q1 and Q3 to get the coefficient.
Step-by-step explanation:
To find the quartile deviation and its coefficient of the given data (Marks obtained: 70, 60, 50, 63, 78.3), we must first arrange the data in ascending order, compute the first and third quartiles (Q1 and Q3), and then calculate the quartile deviation and its coefficient.
- Arrange the data in ascending order:
50, 60, 63, 70, 78.3
- Since we have five data points, the median (second quartile, Q2) is the middle value, which is 63.
- The first quartile (Q1) is the median of the lower half of the data not including the median of the dataset. The lower half is 50, 60, so Q1 is the average of these two numbers: (50 + 60) / 2 = 55.
- The third quartile (Q3) is the median of the upper half of the data not including the dataset median. The upper half is 70, 78.3, hence Q3 is (70 + 78.3) / 2 = 74.15.
- The quartile deviation, also known as the semi-interquartile range, is calculated as (Q3 - Q1) / 2 = (74.15 - 55) / 2 = 9.575.
- To find the coefficient of quartile deviation, divide the quartile deviation by the average of Q1 and Q3: (Q3 + Q1) / 2 = (74.15 + 55) / 2 = 64.575. The coefficient is quartile deviation divided by this average: 9.575 / 64.575 = 0.1482.