Final answer:
To find the usual minimum and maximum using the IQR of 0.69, the formulas Usual minimum = Q1 - (1.5 × IQR) and Usual maximum = Q3 + (1.5 × IQR) are used.
Step-by-step explanation:
When calculating the usual minimum and usual maximum values in a dataset, it's common to use the Interquartile Range (IQR) to locate potential outliers or to describe the spread of the central part of the data.
Although the provided information does not explicitly give the first quartile (Q1) and the third quartile (Q3), you typically find the usual min (lower bound) and usual max (upper bound) using the following formulas:
- Usual minimum = Q1 - (1.5 × IQR)
- Usual maximum = Q3 + (1.5 × IQR)
In your case, the IQR is provided as 0.69. Without Q1 and Q3, we cannot compute the exact usual min and max. If you can find or calculate Q1 and Q3 from your dataset, you'd plug those values and the given IQR into the formulas to find the usual min and max. For instance, if Q1 were 5 and Q3 were 5.69, then:
- Usual minimum = 5 - (1.5 × 0.69) = 5 - 1.035 = 3.965
- Usual maximum = 5.69 + (1.5 × 0.69) = 5.69 + 1.035 = 6.725
Remember to always scrutinize your dataset for any errors or outliers that may affect the calculation of quartile values and consequently the IQR and usual min/max values.