Final answer:
To find the middle of a known population in a data set, the median should be used. The median accurately divides the data set into two equal parts. In skewed distributions, the median is preferred over the mean, as it is less affected by outliers.
Step-by-step explanation:
To determine the scores that mark the middle of a known population, one should use the median. The median is the value that divides the data set into two equal halves, with half of the data being above this value and half being below it. For instance, if we have the data set 10; 11; 15; 15; 17; 22, the median is calculated by taking the average of the two middle values 15 and 15, resulting in a median of 15.
In a symmetrical distribution, the mean, median, and mode are all equal or very close to each other, indicating a balanced distribution of data. However, in skewed distributions, the mean is pulled towards the tail, and the median lies between the mean and the mode, with the mode being the peak of the distribution.
When considering the most appropriate measure of center for a data set, one must examine the shape of the data and look for outliers. In the presence of outliers, such as in the house values data set 45; 47; 47.5; 51; 53.5; 125, the median often provides a better reflection of the central tendency than the mean.