Find the IQR of the data set: 90,99,82,79,100,85,95.
To find the IQR (interquartile range), we first need to find the median of the data set.
Arranging the data set in order:
79, 82, 85, 90, 95, 99, 100
The median is the middle number, which is 90.
Next, we need to find the first quartile (Q1) and the third quartile (Q3).
To find Q1, we take the median of the data set from the first half:
79, 82, 85, 90
The median of this data set is 83.5, which is the first quartile (Q1).
To find Q3, we take the median of the data set from the second half:
95, 99, 100
The median of this data set is 99, which is the third quartile (Q3).
Now we can calculate the IQR:
IQR = Q3 - Q1
IQR = 99 - 83.5
IQR = 15.5
Therefore, the interquartile range of this data set is 15.5.
To find the interquartile range (IQR) of a data set, you need to follow these steps:
Step 1: Arrange the data set in ascending order:
79, 82, 85, 90, 95, 99, 100
Step 2: Find the first quartile (Q1):
To find Q1, you need to locate the median of the lower half of the data set. In this case, the lower half is: 79, 82, 85. Since there is an odd number of values, the median will be the middle value, which is 82. Therefore, Q1 = 82.
Step 3: Find the third quartile (Q3):
To find Q3, you need to locate the median of the upper half of the data set. In this case, the upper half is: 90, 95, 99, 100. Since there is an even number of values, you need to find the average of the two middle values. The two middle values are 95 and 99, so the average is (95 + 99) / 2 = 94. Therefore, Q3 = 94.
Step 4: Calculate the IQR:
The IQR is equal to Q3 - Q1. Hence, IQR = 94 - 82 = 12.
Therefore, the interquartile range (IQR) of the given data set is 12.
To find the IQR (Interquartile Range) of a data set, you need to arrange the data in ascending order and then find the difference between the values of the first quartile (Q1) and the third quartile (Q3).
First, let's arrange the data in ascending order:
79, 82, 85, 90, 95, 99, 100
Next, let's find the values of Q1 and Q3.
1. Find the median of the lower half of the data set: 79, 82, 85. The median is 82.
2. Find the median of the upper half of the data set: 95, 99, 100. The median is 99.
So, Q1 = 82 and Q3 = 99.
To find the IQR, subtract Q1 from Q3:
IQR = Q3 - Q1
IQR = 99 - 82
IQR = 17
Therefore, the IQR of the data set is 17.