Ms.Sue
What 2 aspects of the data determine which measure of central tendency use?
Mean requires relatively normal distribution.
Mode needs multiple scores in some intervals.
To determine which measure of central tendency to use, you need to consider two aspects of the data: the level of measurement and the distribution of the data.
1. Level of measurement: The level of measurement refers to the type of data you have. There are three common levels of measurement: nominal, ordinal, and interval/ratio.
- For nominal data: Nominal data consists of categorical variables without any inherent order or numerical meaning. For example, data on the colors of cars (e.g., red, blue, green) or the names of cities. In this case, you should use the mode as the measure of central tendency.
- For ordinal data: Ordinal data consists of categorical variables that have a specified order or ranking. Examples can include ratings on a Likert scale (e.g., strongly disagree to strongly agree) or education levels (e.g., high school, bachelor's, master's). In this case, you may use the mode, median, or both, depending on the specific requirements of your analysis.
- For interval/ratio data: Interval and ratio data are numeric variables with meaningful numerical values and equal intervals between them. Examples can include temperature in Celsius or the weight of individuals. In this case, you can use the mean, median, or mode, depending on the shape of the distribution.
2. Distribution of the data: The distribution of the data refers to how the values are spread or clustered. It can be symmetric, skewed to the right or left, or have outliers.
- If the distribution is symmetric: For symmetric distributions, you can use the mean, median, and mode interchangeably. They will all provide similar results.
- If the distribution is skewed or contains outliers: In these cases, it is often recommended to use the median as a measure of central tendency. The median is less influenced by extreme values or asymmetrical distributions than the mean.
In summary, the two aspects to consider when choosing a measure of central tendency are the level of measurement and the distribution of the data.