Apsychologist has collected some data on the number of friends that college students report they have. the data set follows: 6, 4, 3, 2, 7, 3, 8, 5. if the psychologist reports 3 as a measure of central tendency, which measure was used?

If 3 was listed as a measure of central tendency, then the mode was used.

The mode is the value that appears most often in the data; this is 3.
The median is the middle value after the data has been ordered from least to greatest.  From least to greatest the data is
2,3,3,4,5,6,7,8

Since there are 8 data values, the median is between 4 and 5:
(4+5)/2 = 9/2 = 4.5

The mean is found by adding the data values and dividing by the number of data values:
(2+3+3+4+5+6+7+8)/8 = 38/8 = 4.75

The range is the difference between the least and greatest:
8-2 = 6

The only one of these that is 3 is the mode.