Central Tendency
Which measure of central tendency is most affected by an extreme score/outlier?
A. Mean
B. Median
C. Mode
D. Range
Mean
In a class of 50 students, 10 received an A.
What percentage received an A?
20% received an A
Two classes have:
Class A: Mean = 75, SD = 4
Class B: Mean = 75, SD = 11
Which class has greater variability?
Class B, because it has the larger standard deviation.
A student has a z-score of +1.5.
What does this tell us?
A. The score is above the mean
B. The score is below the mean
C. The score equals the mean
D. We cannot tell
A. Score is above the mean
A person's blood type is recorded as:
A, B, AB, or O
What level of measurement is this?
A. Nominal
B. Ordinal
C. Interval
D. Ratio
Nominal
The number of hours 7 students studied was:
2, 3, 3, 4, 5, 6, 12
Find the:
A. Mean
B. Median
C. Mode
Answer: Mean = 5, Median = 4, Mode = 3
Use the frequency distribution:
Score Frequency 5:2, 6:3, 7:4, 8:1
How many total observations are represented?
10
Calculate the range:
4, 7, 9, 10, 13, 18
18−4=14
An exam has:
Mean = 80
SD = 5
Student's score = 85
Calculate the z-score.
The student scored 1 standard deviation above the mean.
A researcher records:
5, 6, 6, 7, 8, 10
A. What is the mode?
B. If a score of 30 were added, which would be affected more—the mean or median?
Mode: 6
Mean- more sensitive to extreme values
Employee salaries are:
$35,000, $38,000, $40,000, $42,000, $45,000, $50,000, $250,000
Which measure of central tendency would best represent a typical employee's salary, and why?
Median ($42,000) because the $250,000 outlier would pull the mean upward.
A professor records:
Grade Frequency: A:8, B:12, C:15, D:5
Find:
A. The proportion receiving a B
B. The percentage receiving a B
C. The most frequently occurring grade
A. 0.30
B. 30%
C. C
Consider:
Group A: 48, 49, 50, 51, 52
Group B: 30, 40, 50, 60, 70
Both groups have a mean of 50.
Without calculating standard deviation, determine which group has the larger standard deviation and explain why.
Its scores are much farther from the mean, meaning it has greater variability.
Two students take different exams.
Student A:
Score = 88
Mean = 80
SD = 4
Student B:
Score = 92
Mean = 80
SD = 8
Who performed better relative to their class?
Student A
Two students take different versions of an exam.
Taylor:
Score = 80
Mean = 70
SD = 5
Morgan:
Score = 91
Mean = 85
SD = 3
Calculate both z-scores and determine who performed better relative to their class.
They performed equally well relative to their respective classes. Both scored 2 standard deviations above their class mean.