Final answer:
To calculate the mean, median, and mode from a frequency distribution table, multiply each score by its frequency for the mean, find the middle value for the median, and identify the most frequently occurring score for the mode. When combining two equal-sized samples with known means, the mean of the combined sample is the average of the means of the original samples.
Step-by-step explanation:
To find the mean, median, and mode for the scores in the given frequency distribution, you multiply each score by its frequency and then sum those products. To find the mean (average), divide that sum by the total number of scores. The median is the middle score when all scores are listed in order, and the mode is the score that occurs most frequently. If there are two groups of scores with the same mean, and you are combining them into a single set (with an equal number of scores in both groups), the mean of the combined set will be equal to the mean of the original sets.
For two samples each with n = 4, and means M = 8 and M = 16 respectively, the combined mean will also be M = (8+16)/2 = 12, since the total sum of scores from both samples will be divided by the total number of scores (4+4).