PSYC-FP4700 Assessment 2 Worksheet
Assessment 2 – Central Tendency and Probability
Complete the following problems within this Word document. Do not submit other files. Show
your work for problem sets that require calculations. Ensure that your answer to each problem is
clearly visible. You may want to highlight your answer or use a different type color to set it apart.
Problem Set 2.1: Characteristics of the Mean
Criterion: Describe a distribution.
Instructions: Read the following and answer the questions.
Data: To study perception, a researcher selects a sample of participants (n = 12) and asks them
to hold pairs of objects differing in weight, but not in size, one in each hand. The researcher
asks participants to report when they notice a difference in the weight of the two objects. Below
is a list of the difference in weight (in pounds) when participants first noticed a difference.
Answer the following questions based on the data given in the table.
Difference in Weight
4 8
9 5
12 7
6 15
10 4
8 8
1. State the following values for this set of data:
a) Mean 8. First you would find the sum of all weights (4 + 9 + 12 +
6 + 10 + 8 + 8 + 5 + 7 + 15 + 4 + 8 = 96). Then divide 96 by the
number of values in the dataset (12). 96/12=8
b) Median 8. Arrange the numbers in ascending order: 4, 4, 5, 6, 7, 8,
8, 8, 9, 10, 12, 15. Since there are 12 values, the median will be the
average of the 6th and 7th values: (8 + 8) / 2 = 8
c) Mode(s) 8. The the mode is 8 because it is the number that appears
most within the dataset.
2. What is the shape of this distribution? Hint: Use the values of the mean,
median, and mode to infer the shape of this distribution.
When the mean, median, and mode are all equal and located at the same
value (in this case, 8), the distribution is likely to be symmetric and
approximately normal (bell-shaped). In a symmetric distribution, the
1
, values on the left and right sides of the central point are balanced and
mirror each other. The data points tend to cluster around the center, which
is also where the peak of the distribution is located. Therefore, the shape
of this distribution is most likely symmetric and approximately normal.
Problem Set 2.2.a: Interpret Means in a Chart
Criterion: Interpret means in a chart.
Instructions: Read the information below and answer the questions.
Data: General life satisfaction across culture. Gilman and colleagues (2008) measured general
life satisfaction in 1,338 adolescents from two individualistic nations (Ireland, United States) and
two collectivist nations (China, South Korea) using the Multidimensional Students’ Life
Satisfaction Scale (MSLSS). Mean participant scores on the MSLSS are given in the following
table.
Mean MSLSS Scores by Nation and Gender
Nation Gender
Men Women
United States
4.39 4.61
Ireland 4.37 4.64
China 4.41 4.56
South Korea 3.92 3.78
1. Among which group was general life satisfaction lowest on average?
General life satisfaction was lowest among women in South Korea, as 3.78 is the lowest
number on the chart.
2. Among which group was general life satisfaction highest on average?
General life satisfaction was highest among women in Ireland, as 4.64 is the highest
number on the chart.
Problem Set 2.2.b: Understanding Standard Deviations in a Chart
Criterion: Interpret standard deviations in a chart.
Instructions: Read the following and answer the question based on the data in the chart.
2
Assessment 2 – Central Tendency and Probability
Complete the following problems within this Word document. Do not submit other files. Show
your work for problem sets that require calculations. Ensure that your answer to each problem is
clearly visible. You may want to highlight your answer or use a different type color to set it apart.
Problem Set 2.1: Characteristics of the Mean
Criterion: Describe a distribution.
Instructions: Read the following and answer the questions.
Data: To study perception, a researcher selects a sample of participants (n = 12) and asks them
to hold pairs of objects differing in weight, but not in size, one in each hand. The researcher
asks participants to report when they notice a difference in the weight of the two objects. Below
is a list of the difference in weight (in pounds) when participants first noticed a difference.
Answer the following questions based on the data given in the table.
Difference in Weight
4 8
9 5
12 7
6 15
10 4
8 8
1. State the following values for this set of data:
a) Mean 8. First you would find the sum of all weights (4 + 9 + 12 +
6 + 10 + 8 + 8 + 5 + 7 + 15 + 4 + 8 = 96). Then divide 96 by the
number of values in the dataset (12). 96/12=8
b) Median 8. Arrange the numbers in ascending order: 4, 4, 5, 6, 7, 8,
8, 8, 9, 10, 12, 15. Since there are 12 values, the median will be the
average of the 6th and 7th values: (8 + 8) / 2 = 8
c) Mode(s) 8. The the mode is 8 because it is the number that appears
most within the dataset.
2. What is the shape of this distribution? Hint: Use the values of the mean,
median, and mode to infer the shape of this distribution.
When the mean, median, and mode are all equal and located at the same
value (in this case, 8), the distribution is likely to be symmetric and
approximately normal (bell-shaped). In a symmetric distribution, the
1
, values on the left and right sides of the central point are balanced and
mirror each other. The data points tend to cluster around the center, which
is also where the peak of the distribution is located. Therefore, the shape
of this distribution is most likely symmetric and approximately normal.
Problem Set 2.2.a: Interpret Means in a Chart
Criterion: Interpret means in a chart.
Instructions: Read the information below and answer the questions.
Data: General life satisfaction across culture. Gilman and colleagues (2008) measured general
life satisfaction in 1,338 adolescents from two individualistic nations (Ireland, United States) and
two collectivist nations (China, South Korea) using the Multidimensional Students’ Life
Satisfaction Scale (MSLSS). Mean participant scores on the MSLSS are given in the following
table.
Mean MSLSS Scores by Nation and Gender
Nation Gender
Men Women
United States
4.39 4.61
Ireland 4.37 4.64
China 4.41 4.56
South Korea 3.92 3.78
1. Among which group was general life satisfaction lowest on average?
General life satisfaction was lowest among women in South Korea, as 3.78 is the lowest
number on the chart.
2. Among which group was general life satisfaction highest on average?
General life satisfaction was highest among women in Ireland, as 4.64 is the highest
number on the chart.
Problem Set 2.2.b: Understanding Standard Deviations in a Chart
Criterion: Interpret standard deviations in a chart.
Instructions: Read the following and answer the question based on the data in the chart.
2
