Psyc202 Chapter 3 – Central Tendency
Descriptive Statistics: organize and summarize data/scores
Central Tendency: a statistical measure to determine a single score that defines
the center of a distribution. The goal of central tendency is to find the single score
that is most typical or most representative of the entire group. (“the average”)
3 methods for measuring central tendency: mean, median, mode
Mean: sum of the scores divide by the number of scores (‘N’).
o Mean of population = mew μ
o Mean of sample = xbar, identified by M or x̄
o Formula for population : μ= ∑X
o Formula for sample: M = ∑X
o 2 use for mean: when don’t know the exact scores, assume the mean is
the equally distributed score for everyone. Example: a sample size of 12
with a mean of 6. Since you don’t know the individual scores, assume all
12 people have a score of 6.
Weighted Mean: combining the mean of 2 or more separate groups. This mean
is not exactly the average, as it tends to be closer to one group’s average than
another. (see notebook for solution to p.76)
o Weighted Mean = Combined Sum of groups = ∑X +∑X 1 2
Combined n = 1 + n2
Changing a score or ‘n’ always changes the value of the mean. Exception: when
the new score is exactly equal to the mean.
If a constant value is added/subtracted from every score in the distribution, the
same constant will be added to the mean. Same thing goes with multiplication and
division (**Only if ALL scores in distribution have the same thing applied)
Median: the score that divides a distribution in half so that 50% of the individuals
in a distribution have scores at or below the median. If scores listed in order,
median is the midpoint of the list.
Median calculations and notations are same for population and sample.
When ‘n’ is an even number, the median is found by averaging the 2 middle
Finding Median for a Continuous Variable:
o Start by creating block bar graph to represent score data.
o Find precise midpoint by finding half of n (ex. N=10, so look for the score
at 5 blocks from the left)
o If more than one box stacked on top of middle column, only take a
fraction of all the boxes, so that together the fractions all add up to 1. (ex.
5 boxes when we need one… use 1/5 of all the boxes.)
o Draw a vertical line down these separating the used fraction of the boxes
from the unused fraction. o Find the range of the lower real limit and the upper real limit (ex. 3.5 and
4.5 if the middle box you need is at ‘4’. Range here = 1). And multiply the
range by the fraction of boxes being used (ex. 1/5(1) = 0.2). Add that
amount to the lower real interval (ex. 3.5+0.2=3.7) and that’s where you
would draw your line; the exact middle point of the interval.
o NOTE: this is only for continuous variables (like time, distance) not for
discrete variables (like number of children in a family). For discrete
variables, just list numbers and order and find middle number.