The following quiz scores measured as a discrete variable are as follows: 2, 4, 2, 5, 6, 3, 4. Find the range and the interquartile range (IQR)?
1 Answer
The range is 4 and the IQR is 3.
Explanation:
First, sort the quiz scores in ascending order: 2, 2, 3, 4, 4, 5, 6. The range of the quiz scores is the difference between the highest and lowest scores, which is 6 - 2 = 4.
To find the IQR, we need to find the first, second (median), and third quartiles. The median is the "middle" score of the quizzes, and in this case is 4 because in the distribution of quiz scores, 3 scores are less than/equal to 4 and 3 scores are greater than/equal to 4.
To find the first and third quartiles, we find the median of the data set to the left of 4 and to the right of 4, respectively, giving us the first quartile of 2 and the third quartile of 5. Finally, the IQR is the difference of the third and first quartiles which is 5 - 2 = 3.
