Given:
The given set of data is 51, 62, 73, 92, 97, 100, 104.
The objective is to find Q1,Q2, Q3 the midquartile, and the interquartile range.
Step-by-step explanation:
The given set of data is already arranged in increasing oder.
To find Q2:
The quartile Q2 represents the middle term of the set of data arranged in increasing order.
The number of terms in the set of data is N = 7.
Then, the middle term of the set of data is 92, which is Q2.
To find Q1:
The quartile 1 represents the middle term of the left side of the Q2.
The left side of Q2 contains 51, 62, 73.
Thus, the middle term of the left side of Q2 is 62, which is Q1.
To find Q3:
The quartile 3 represents the middle temr of the right side of the Q2.
The right side of Q2 contains 97, 100, 104.
Thus, the middle term of the right side of Q2 is 100, which is Q3.
To find midquartile:
The midquartile is termed as the average of highest and lowest value of the set of data.
The highest value in the given set of data is 104 and the lowest value in the given set of data is 51.
Then, the midquartile can be calculated as,
To find interquartile:
The