Suppose, we have 5 observations such that 29, 48, 30, 35, 99. Calculate the Inter Quartile Range (IQR) of the data.19184849
Question
Suppose, we have 5 observations such that 29, 48, 30, 35, 99. Calculate the Inter Quartile Range (IQR) of the data.19184849
Solution 1
To calculate the Interquartile Range (IQR), we first need to order the data from smallest to largest and then find the quartiles.
Step 1: Order the data The ordered data is: 29, 30, 35, 48, 99
Step 2: Find the quartiles Since we have 5 observations, the second quartile (Q2), also known as the median, is the middle number, which is 35.
The first quartile (Q1) is the median of the lower half of the data (not including Q2 if the number of observations is odd). In this case, the lower half is 29 and 30, so Q1 is the average of these two numbers: (29+30)/2 = 29.5
The third quartile (Q3) is the median of the upper half of the data (not including Q2 if the number of observations is odd). In this case, the upper half is 48 and 99, so Q3 is the average of these two numbers: (48+99)/2 = 73.5
Step 3: Calculate the IQR The IQR is the difference between Q3 and Q1: IQR = Q3 - Q1 = 73.5 - 29.5 = 44
So, the Interquartile Range (IQR) of the data is 44.
Solution 2
To calculate the Inter Quartile Range (IQR), we first need to order the data from smallest to largest.
So, the ordered data is: 29, 30, 35, 48, 99.
Next, we need to find the first quartile (Q1) and the third quartile (Q3).
Since we have
Solution 3
To calculate the Interquartile Range (IQR), we first need to order the data from smallest to largest and then find the quartiles.
Step 1: Order the data The ordered data is: 29, 30, 35, 48, 99
Step 2: Find the quartiles The median (Q2) is the middle value of the ordered data. Since we have 5 observations, the median is the 3rd value, which is 35.
The lower quartile (Q1) is the median of the lower half of the data (not including the median if the number of observations is odd). In this case, the lower half of the data is 29 and 30, so Q1 is (29+30)/2 = 29.5.
The upper quartile (Q3) is the median of the upper half of the data (not including the median if the number of observations is odd). In this case, the upper half of the data is 48 and 99, so Q3 is (48+99)/2 = 73.5.
Step 3: Calculate the IQR The IQR is Q3 - Q1, so in this case, the IQR is 73.5 - 29.5 = 44.
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