The list shows the number of employees at seven companies. 525, 650, 539, 643, 764, 539, 687 What is the interquartile range of these numbers??
To find the interquartile range, we need to find the first quartile (Q1) and the third quartile (Q3).
First, let's arrange the numbers in ascending order: 525, 539, 539, 643, 650, 687, 764
The median is the middle value, which is 643.
Let's find Q1, which is the median of the lower half of the data set: 525, 539, 539, 643
The middle value of this subset of data is the average of the two middle values: (539 + 539)/2 = 539
Now let's find Q3, which is the median of the upper half of the data set: 643, 650, 687, 764
Similarly, the middle value of this subset of data is the average of the two middle values: (650 + 687)/2 = 668.5
Now we can calculate the interquartile range: Q3 - Q1 = 668.5 - 539 = 129.5
Therefore, the interquartile range of these numbers is 129.5.
wrong
Apologies for the error. Let's find the correct interquartile range.
First, let's arrange the numbers in ascending order: 525, 539, 539, 643, 650, 687, 764.
Next, we need to find the first quartile (Q1) and the third quartile (Q3).
To find Q1, which is the median of the lower half of the data set, we need to find the median of the numbers less than the overall median (643): 525, 539, and 539.
The median of this subset is (525 + 539) / 2 = 532.
To find Q3, which is the median of the upper half of the data set, we need to find the median of the numbers greater than the overall median (643): 650, 687, and 764.
The median of this subset is (650 + 687) / 2 = 668.5.
Finally, we can calculate the interquartile range by subtracting Q1 from Q3: 668.5 - 532 = 136.5.
Therefore, the correct interquartile range of these numbers is 136.5.
To find the interquartile range (IQR), you first need to determine the lower quartile (Q1) and the upper quartile (Q3).
Step 1: Arrange the numbers in ascending order:
525, 539, 539, 643, 650, 687, 764
Step 2: Calculate the median (Q2) of the data set. In this case, since there is an odd number of values, the middle number is the median.
Median = 643
Step 3: Divide the data set into two halves: the lower half and the upper half.
Lower half: 525, 539, 539
Upper half: 650, 687, 764
Step 4: Calculate the median of each half.
Lower quartile (Q1) = Median of the lower half = 539
Upper quartile (Q3) = Median of the upper half = 687
Step 5: Calculate the interquartile range (IQR):
IQR = Q3 - Q1
IQR = 687 - 539
IQR = 148
Therefore, the interquartile range of the given numbers is 148.