PSYC 510
HOMEWORK: Z-SCORES AND PERCENTILES TEMPLATE
This assignment is worth a total of 60 points.
•Content: point values vary but are indicated in the template and total 45 points.
•Format: point values vary but are indicated in the template for 10 pts. The remaining 5
pts are for placing answers in the correctly designated spots within the template in a clear
and easy to read format (e.g., all fit within the visible screen on the page) and uploading it
in an approved format (word or PDF). Thus, the maximum is 15 points for format.
Here is memory data from 25 students. Create an SPSS data file using this data.
8 6 7 5 5
5 6 8 5 3
6 9 5 9 7
6 5 6 4 8
8 7 10 6 6
1
.
Name the variable “Memory” in Variable View and set the scale of
measurement. Run descriptive statistics to obtain the needed mean and
standard deviation and other information to determine whether the data is
normally distributed. Make sure to “save standardized values” when
doing so. Copy / Paste the output here, formatting using professional
conventions, numbering it as Table 1 and giving it an appropriate title (no
Note needed). (4 pts content / 3 pt format)
Descriptive Statistics
N Mean
Std.
Deviation
Memory 25 6.4000 1.68325
Valid N
(listwise)
25
2. Create an appropriate figure to examine the
distribution of memory scores in the sample
(make sure both axes titles are in Title Case!).
Number it Figure 1 and create an appropriate title. In
the Note section, using both a visual inspection of the
data and a skewness statistic to discuss whether the
distribution is normal. Make sure all components are
formatted using APA conventions. (4 pts content / 3
pts format)
Page 1 of 4
PSYC 510
3. Determine whether memory scores in this sample are normally distributed. State whether it
is normally distributed and what information you used to determine this. (2 pts)
5. Continuing to use this dataset, go to Variable View, create a third variable and name it
“percRank”. Have SPSS compute the percentile ranks based on the normal distribution,
Based on the scores, the distribution appears to be quite normal. There’s a slight increase in the
number of scores clustered around five and six, but overall, the scores are spread across the range
and are not heavily skewed toward one side. The majority of scores fall in the middle, which
reflects a typical bell-curve distribution. This pattern indicates a well-balanced dataset without
any extreme outliers or significant skewness.
4. Write a brief description of the memory scores obtained from this sample as you would in
a Method section of a research report. Use proper APA format as shown in previous
weeks. (4 pts content / 2 pts format)
In this study, memory scores were obtained from a group of 25 participants. The distribution of
scores was close to normal, as indicated by skewness (0.273) and kurtosis (-0.241) values. The
group’s mean memory score was 6.4 with a standard deviation of 1.68, suggesting participants
generally performed well, with most individual scores clustering near the average and only minor
variation across the sample.
using the Mean and Standard Deviation shown in your output from Question #1 (rounding
to two decimal places). Organize your dataset by using the “Sort Cases” by zscores
Page 2 of 4
PSYC 510
ascending as shown in this week’s lecture video. Take a snapshot of your data view and
place it below so that all three columns can be seen in their entirety. (This does not need to
be in APA format). (3 pts content / 2 pts format)
6. Assuming a normal distribution, use the output shown in your answer above to answer the
following questions: (3 pts each = 12 pts content)
A. Identify the memory score values in the
data set that are above the 50th percentile.
Data set number is 8. Memory scores above the mean
(6.40) include: 7,8,9, and 10. Above 50th percentile.
B. Are the corresponding z scores below zero,
near zero, or above zero? Why (discuss in
relation to the mean)?
Above zero; mean: (6.40) 1.47291/1.90 = .77
C. Identify all scores that are in the bottom
10th percentile.
Data set number is 6. Scores such as 3 and 4 fall within the bottom
10th percentile, based on low Z scores and relative position in the
distribution.
D. Are the corresponding z scores below zero,
near zero, or above zero? Why (discuss in
relation to mean)?
Below zero. The mean is (6.40) -0.10521
/ 1.90 =0.06
7. Assuming a normal distribution, use the mean and standard deviation you obtained from
the SPSS output in previous sections to answer the following questions:
Note: you MUST show all work to be eligible for credit. Round to 2 decimals for z score; do
NOT round the proportion values you get from Appendix C.3 – provide all 4 decimals as
shown in the table. (4 pts each = 8 pts Content)
A. Calculate the z-score for a memory score of 7.5 (round to two decimal places)
Z = (7.5-6.40)/1.90 = 0.578 = 58 P
= 6/7 = 0.8571 x 100 = 85.71
B. Given the z score you calculated for a memory score of 7.5, find the proportion of the
distribution located up to this point. (Hint: remember if the z score is above the mean, you’ll
need to add 0.50!) **do NOT round – provide all 4 decimal places**
0.58 +.50 = 1.08
Page 3 of 4
PSYC 510
8. Assuming a normal distribution, use the mean and standard deviation you obtained from
the SPSS output in previous sections to answer the following questions:
Note: you MUST show all work to be eligible for credit. Round to 2 decimals for z score; do
NOT round for proportion – use all 4 decimals as shown in Appendix C.3. (4 pts each = 8
pts total)
A. For a memory score of 4.5, calculate the z-score.
Z = (4.5-6.40)/1.90 = -1
B. Given the z score you calculated for a memory score of 4.5, find the proportion of the
distribution located up to this point. **Think about what C.3 provides (area between the mean
and z) and where your point would fall on the normal distribution. You will need to subtract
the number you find in the table from 0.5 to answer this question. Do NOT round – show all
work – final answer should have 4 decimal places.
P = -1.11315 - 0.5 = 1.6315
Note: Your assignment will be checked for originality via the Turnitin plagiarism tool.
Page 4 of 4
