Final answer:
To identify outliers in the data set, calculate the IQR and then determine values outside of 1.5 * IQR from the first and third quartiles.
Step-by-step explanation:
To find out the outliers from the given data set, we typically use a statistical test involving the Interquartile Range (IQR). An outlier is a data value that is distinctly separate from the rest of the data. It could be much higher or much lower than the rest of the data points. One common rule for determining outliers is to find values that are more than 1.5 * IQR above the third quartile or below the first quartile.
Let's calculate the IQR for the data set 14.7, 15.1, 14.5, 15.9, 14.6, 14.5, 14.4, 14.4, 10.2, 14.7, 16.4, 14.9, 14.1, 14.4, 14.7:
- First, arrange the data in ascending order.
- Then, find the first quartile (Q1), the median, and the third quartile (Q3).
- Calculate the IQR by subtracting Q1 from Q3.
- Find 1.5 * IQR and add it to Q3 to get the upper bound, and subtract it from Q1 to get the lower bound.
- Any value outside these bounds is considered an outlier.
Without a complete set of calculations, we cannot provide the exact outliers, but we can conclude that data points like 10.2, which are significantly lower than the rest, might be potential outliers. It should be noted if there are significant deviations such as those identified above, it may affect calculations like mean, and therefore, skewing data analysis and interpretation.
When outliers are identified, they should be carefully examined. If they are legitimate data points (not data entry errors or caused by extraordinary circumstances), they should typically be included in the data analysis, as they may represent important variation in the data set.