Name:
GNRS 613: Graduate Statistics
Midterm Exam
Hint: Please review z scores.....note that a score needs to be +/- 2 sd from the mean (or
+/- a z score of 2) to be considered significant. There are a few questions on the exam
related to this. I would like for you to work out the answers first.
Please answer each of the following questions.
1. For the data below, tell me the mean, median, mode, and standard deviation.
The Data:
102.5, 104.5, 100.4, 95.9, 87, 95, 88.6, 89.2, 78.9, 84.6, 81.7, 72.2, 65.1, 68.1, 67.3, 52.5
The number of observations is 16
i. Mean = (102.5 + 104.5 + 100.4 + 95.9 + 87 + 95 + 88.6 + 89.2 + 78.9 + 84.6
+ 81.7 + 72.2 + 65.1+ 68.1 + 67.3 + 52.5)/16 = 83.34375
ii. Median = (84.6+87)/2 = 85.8
iii. Mode = There is no mode amongst the given numbers
iv. Standard deviation
The formulae for calculating variance =
Substituting the values:
Variance = 212.2774609
, Name:
Standard deviation = √ variance
= √ 212.2774609
= 14.5697
2. For the data below, tell me the mean, median, mode, and standard deviation.
25, 24, 26, 31, 35, 38, 26, 24, 27, 26, 34, 36, 33, 31, 30
In this second question, we can use excel to solve it:
i. Mean = 29.73333
ii. Mode = 26
iii. Median = 30
iv. Standard deviation = 4.667007
For the three questions below…..think z scores and the area under the curve.
3. A nursing professor was curious as to whether the students in a very large
class she was teaching who turned in their tests first scored differently from
the overall mean on the test. The overall mean score on the test was 75 with
a standard deviation of 10; the scores were approximately normally
distributed. The mean score for the first 20 tests was 78. Did the students
turning in their tests first score significantly different from the mean?
Explain.
Overall mean = 75
The standard deviation = 10
The mean score for the first 20 tests was 78
We are testing the mean of the first 20 tests, whether it is significantly different from the
overall mean of the tests.
GNRS 613: Graduate Statistics
Midterm Exam
Hint: Please review z scores.....note that a score needs to be +/- 2 sd from the mean (or
+/- a z score of 2) to be considered significant. There are a few questions on the exam
related to this. I would like for you to work out the answers first.
Please answer each of the following questions.
1. For the data below, tell me the mean, median, mode, and standard deviation.
The Data:
102.5, 104.5, 100.4, 95.9, 87, 95, 88.6, 89.2, 78.9, 84.6, 81.7, 72.2, 65.1, 68.1, 67.3, 52.5
The number of observations is 16
i. Mean = (102.5 + 104.5 + 100.4 + 95.9 + 87 + 95 + 88.6 + 89.2 + 78.9 + 84.6
+ 81.7 + 72.2 + 65.1+ 68.1 + 67.3 + 52.5)/16 = 83.34375
ii. Median = (84.6+87)/2 = 85.8
iii. Mode = There is no mode amongst the given numbers
iv. Standard deviation
The formulae for calculating variance =
Substituting the values:
Variance = 212.2774609
, Name:
Standard deviation = √ variance
= √ 212.2774609
= 14.5697
2. For the data below, tell me the mean, median, mode, and standard deviation.
25, 24, 26, 31, 35, 38, 26, 24, 27, 26, 34, 36, 33, 31, 30
In this second question, we can use excel to solve it:
i. Mean = 29.73333
ii. Mode = 26
iii. Median = 30
iv. Standard deviation = 4.667007
For the three questions below…..think z scores and the area under the curve.
3. A nursing professor was curious as to whether the students in a very large
class she was teaching who turned in their tests first scored differently from
the overall mean on the test. The overall mean score on the test was 75 with
a standard deviation of 10; the scores were approximately normally
distributed. The mean score for the first 20 tests was 78. Did the students
turning in their tests first score significantly different from the mean?
Explain.
Overall mean = 75
The standard deviation = 10
The mean score for the first 20 tests was 78
We are testing the mean of the first 20 tests, whether it is significantly different from the
overall mean of the tests.
