1. What two aspects of the data determine which measure of central tendency to use?
2. Why is it best to use the mean with a normal distribution ?
Questions are from chapter 4 Basic Statistics for the Behavioral Sciences 7th edition
wfafawfadf
1. The two aspects of the data that determine which measure of central tendency to use are the level of measurement and the shape of the distribution.
The level of measurement refers to the type of data being analyzed, which can be categorical (nominal or ordinal) or numerical (interval or ratio). Different measures of central tendency are appropriate for different levels of measurement. For categorical data, the mode is typically used to represent the central tendency. For numerical data, measures such as the mean, median, or mode can be used, but the choice depends on the shape of the distribution as well.
The shape of the distribution refers to the way the data is distributed around the central tendency. If the data is normally distributed, meaning it follows a symmetrical bell-shaped curve, then the mean is the most appropriate measure of central tendency. If the data is heavily skewed or has extreme outliers, the median might be a better representation of the central tendency. The mode can be useful for identifying the most frequently occurring value in any type of distribution.
2. It is best to use the mean with a normal distribution because the mean is a measure of central tendency that takes into account every data point in the distribution.
In a normal distribution, the data is symmetrically distributed around the mean, with roughly 68% of the data falling within one standard deviation from the mean, 95% falling within two standard deviations, and 99.7% falling within three standard deviations. This symmetrical nature of the normal distribution makes the mean an ideal representation of the central tendency.
Moreover, the mean is a powerful tool when analyzing normally distributed data as it takes into account the magnitude of each data point. This property makes it essential for various statistical calculations and techniques, such as hypothesis tests and regression analysis, which rely on the mean as a measure of central tendency.
However, it's important to note that the mean can be heavily influenced by outliers or skewed distributions. Therefore, in cases where the data is not normally distributed or has extreme values, it might be more appropriate to use other measures of central tendency, such as the median or mode.