Measures of Center
Descriptive Statistics
• Describing the samples by its statistic
• Measures of Center
• Mean
• Median
• Mode
Mean
• Measured the center of the data by adding the data values and dividing by the total number of data values.
• Sensitive to extreme value
• Reliable
• Take account all the data
Example
From Mario (2012), Exercise #20, p. 96.
Radiation in Baby Teeth. Listed below are amounts of strontium-90 (in millibecquerels or mBq per gram of calcium) in a simple random sample of baby teeth obtained from Pennsylvania residents born after 1979
(based on data from “An Unexpected Rise in Strontium-90 in U.S.
Deciduous Teeth in the 1990s,” by Mangano, et al., Science of the Total Environment). How do the different measures of center compare?
What, if anything, does this suggest about the distribution of the data?
Data
155 142 149 130 151 163 151 142 156 133 138 161 128 144 172 137 151 166 147 163 145 116 136 158 114 165 169 145 150 150 150 158 151 145 152 140 170 129 188 156
Median
• Middle value
• If the number of data values is odd, median = the exact middle of the list
• If the number of data values is even, median = the mean of the two middle numbers
• Not sensitive to extreme value
Mode
• Data value that occurs with the greatest frequency
• Unimodal
• Bimodal
• Multimodal
• No mode
Mean from Frequency Distribution
• Estimation of the mean
• Not always equal to the actual mean
• Assuming that all sample values in each class/interval equal to the class midpoint
What next?
• Read the next module or chapter about measures of variation or dispersion
• There will be a quiz next week (on Monday).
• For those of you who scored less than 80 on their Quiz #1 please let me know if there is anything I can help you with.
