Final answer:
The IQR cannot be directly calculated from the mean and standard deviation, but if the data follows a normal distribution, you can estimate the IQR by finding the values that lie 0.6745 standard deviations below and above the mean and then subtracting the first quartile from the third quartile.
Step-by-step explanation:
It is not directly possible to find the Interquartile Range (IQR) using only the mean and standard deviation, as the IQR involves quartile values. However, if you assume a normal distribution, you can estimate the quartiles using the mean and standard deviation.
To find the approximate quartiles in a normal distribution:
- The first quartile (Q1) can be estimated by finding the value that lies 0.6745 standard deviations below the mean. Use the formula Q1 = mean - 0.6745 × standard deviation.
- The third quartile (Q3) is the value that lies 0.6745 standard deviations above the mean. So, Q3 = mean + 0.6745 × standard deviation.
- Then, calculate the IQR by subtracting the first quartile from the third quartile: IQR = Q3 - Q1.
An example of finding the IQR: If the mean is 1,809.3 and the standard deviation is 151.2, the estimated first quartile would be 1,809.3 - (0.6745 × 151.2) and the estimated third quartile would be 1,809.3 + (0.6745 × 151.2). Subtract the first quartile value from the third quartile value to obtain the IQR.