Counseling Duration

Mean, Median, Mode, and Cumulative Percentage Statistical Guide

The mean (M) is the average that is the balance point in a distribution. It is calculated bysumming all the scores and dividing by the number of scores. The mean is pulled toward extreme scores in an unbalanced distribution (i.e., a skewed distribution, with extreme scores on one side and without extreme scores on the other side to balance it).

The median (Mdn) is the average that indicates the value below which half of the cases lie.For instance, if the median for a group is 10.0, then 50% of the cases lie below 10.0. The median is not pulled toward extreme scores in a skewed distribution.

The mode is the most frequently occurring score. For instance, if more individuals have a
score of 29 than have any other score, then 29 is the mode.

See the previous exercise for the definition of cumulative percentage. A common symbol for
cumulative percentage is cum%. Because a cumulative percentage is calculated by summing per-
centages, an alternative symbol is 2%, which is shown in the table in the excerpt. Note that the
Greek letter 2 means sum of in statistics.

The f in the table in the excerpt means frequency, which indicates how many had each score.

“Scores” are not always “test scores” in statistics. In the excerpt, the scores are “number of
sessions completed.” Thus, if a client completes 10 sessions, his or her score is 10. The scores in the
table in the excerpt have been grouped. For instance, “l-3” in the first column in the table represents
this group of scores: 1, 2, and 3.

Excerpt from the Research Article‘

During an academic year, new clients at a university counseling center were recruited to par-
ticipate in this study. All new clients requesting individual counseling services were eligible to par-
ticipate. Ninety-four new clients (the majority of new clients at the center) agreed to participate…
The ages of the participants ranged from 18 years to 47 years (Mdn = 21.00, M = 22.4.

Table 1 presents a frequency distribution of counseling duration. Participants completed from
1 to 28 sessions (Mdn = 3.0, M = 4.6. . .). As evident in the table, most participants completed a rela-
tively small number of sessions.

Table 1
Frequency Distribution of Counseling Duration
No. of sessions completed f % 2%
1-3 54 57.4 57.4
4-6 22 23.4 80.8
7-9 8 8.5 89.3
10-12 4 4.3 93.6
14-17 3 3.2 96.8
18-28 3 3.2 100.0
Note. Mdn = 3, Mode =1, M= 4.6
Source: Hatchett, G. T. (2003). Does psychopathology predict counseling duration? Psychoiogical Reports, 93,
175-185.
Exercises 11, 16, 17 and 18 Interpreting Basic Statistics

Please read exercise 11 (counseling duration) and complete the following questions (1-8).
1. What is the median number of sessions completed by the participants?
a. 10.0
b. 9.0
c. 3.0
d. 4.6
2. What % of clients was above age 21?
a. 10 %
b. 50%
c. 21%
3. Are the mean and the median age of the participants the same?
a. no
b. yes
4. How many clients completed 4-6 sessions?
a. 8
b. 22
c. 30
d. 84
5. What % of the clients completed 4-6 sessions?
a. 8
b. 8.5
c. 23.4
d. 89.3

6. Is the following statement true or false? “42.6% of the clients completed more than 3 sessions”
a. true
b. false
7. Is the following statement true or false? “96.8% of the clients completed 13 or fewer sessions”
a. true
b. false
8. Is the following statement true or false? “40.8% of the clients completed at 4 but less than 10 sessions”
a. true
b. false
Please read exercise 16(Asian values: mean, standard deviations and 68% rule and complete questions (9-13).
9. Based on report, do boys or girls have a higher median AVS score?
a. boys
b. girls
10. Assuming that the distribution of scores for the study population is normal, what % of participants had scores between 134.4 and 175.8?
a. 50%
b. 68%
c. 95%
d. 97.5%
11.Based on the standard deviations, do boys or girls have less variability in their scores?
a. boys
b. girls
12.Assuming that the distribution of boys scores is normal what % of boys had scores between 135.1 and 152.7?
a.34%
b.68%
c.99%
d.50%
13.Assuming that the distribution of scores for girls is normal the middle 68% of girls had scores between what 2 values?
a.138.6 and 189.4
b.24.7 and 158.3
c.133.6 and 183.0
d.188.9 and 207.7

Please read exercise 17 (college students’ Alcohol knowledge: mean, standard deviation and approximately 95% and 99.7% rules) and complete questions (14-18).

14.On the average which group had higher posttest scores?
a. control group
b. intervention group
15. On the posttest, which group had less variability in scores?
a. control group
b. intervention group
16. On the average, which group showed the greater (mean) gain from pretest and posttest?
a. control group
b. intervention group
17. Assuming that the distribution of posttest scores for the control group is normal, between what 2 values did approximately the middle 95% of the posttest scores for participants in the control group lie?
a. 39.8 and 51.6
b. 70.4 and 96.0
c. 57.6 and 108.8
d. 83.2 and 108.8
18. Assuming that the distribution of posttest scores for the interventional group is normal, what % of the participants had posttest scores between 76.0 and 100.8?
a. 68%
b. 50%
c. 95%
d. 99.7%

Please read exercise 18 (competitiveness and culture: mean, standard deviation and precise 95% and 99% rules) and complete questions (19 to 21).
19. Examine the statistics for “Enjoyment of competition” for women in which national-origin group has the most variability in its scores?
a. United States, because the women from United States have highest mean score
b. United States, because the women from United States have largest standard deviation
c. Japan, because the women from Japan have the smallest deviation
20. The mean score on “Contentiousness” for all women is 14.7, assuming that the distribution of the scores is normal. What % of the cases have scores between 6.9 and 22.5?
a. 50%
b. 68%
c. 95%
d. 99%
21. Which sample is the least heterogeneous in their level of “Enjoyment of competition”?
a. The China Sample
b. The Japan Sample
c. The United States Sample