Final answer:
Outliers are identified using IQR and standard deviation methods. They can influence data analysis significantly and may need to be removed or investigated, depending on the context. Graphing calculators can visually assist in identifying potential outliers in a dataset.
Step-by-step explanation:
In the context of detecting outliers, we use statistical methods to identify data points that differ significantly from the rest of the dataset. One common method for identifying outliers involves the use of the interquartile range or IQR. To calculate the IQR, arrange the data in ascending order and find the quartiles (Q1, Q2, and Q3). The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). Data points that are more than 1.5 times the IQR above the third quartile or below the first quartile are considered outliers.
Another method involves the calculation of the standard deviation. If the data is mound-shaped and symmetric, a data point that is more than two standard deviations away from the mean may be considered an outlier. However, if the distribution of the data is skewed, the standard deviation criteria might not be appropriate.
Outliers can drastically affect the analysis, such as increasing the variance or affecting the slope in a regression analysis. Whether to remove outliers depends on the nature of the data and its significance. In some cases, outliers are errors and should be removed, but they can also contain valuable information about the dataset and should be investigated further.
Using graphing calculators like the TI-83, TI-83+, or TI-84+ can assist in visually identifying outliers by comparing the distance of data points from a line of best fit or a regression line. Any data point that appears to be an abnormal deviation from the rest could be flagged for further examination.