Course assessment
This attempt will impact your course
performance
Homework: Summary statistics,Normal
distribution [now finished]
Total score: 42 out of 44, 95%
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1 of 20 ID: MST.CPD.ND.09.0010c.abe [5 points]
A group of 110 students sat an aptitude test, their resulting scores are presented:
Scores: Download the data
65 67 71 63 68 68 59 66 65 74
66 65 70 68 66 70 72 58 73 64
73 64 68 73 68 75 66 68 69 65
75 74 74 69 69 70 74 59 62 71
77 83 76 79 68 58 74 73 64 75
64 79 70 56 70 54 68 53 72 69
67 54 67 70 55 67 57 76 82 59
60 68 72 62 64 72 68 58 67 79
70 70 70 65 62 64 67 62 71 66
63 60 72 70 69 60 60 69 64 72
71 64 68 72 79 68 65 77 63 62
a) Calculate the mean and standard deviation for the sample. Give your answers to 2 decimal places.
sample mean = 67.68
sample standard deviation = 6.12
b) Find the proportion of scores that are within 1 standard deviation of the sample mean and also the
proportion that are within 2 standard deviations of the sample mean. Use the unrounded values for the
mean and standard deviation when doing this calculation. Give your answers as decimals to 2 decimal
places.
Proportion of scores within 1 standard deviation of the mean = 0.69
Proportion of scores within 2 standard deviations of the mean = 0.95
c) Find the proportion of values in the sample that are less than 70. Give you answer as a decimal to 2
decimal places.
, Proportion of values less than 70 = 0.61
Feedback [5 out of 5]
a) You are correct.
b) You are correct.
c) You are correct.
Discussion
a) Using a statistical software package, the following results can be obtained:
Sample Statistics
sample mean 67.68181818...
sample standard deviation 6.14642705...
Alternatively, the sample mean and standard deviation statistic can be calculated using the
following formulas: show variables
x =
∑xi
n
= 67.68181818...
= 67.68 Rounded as last step
∑ (xi x)2
s2 =
n1
s = 6.14642705...
= 6.15 Rounded as last step
b) From the results in part a) you can now determine that all values within
x ± s = 67.68181818... ± 6.14642705...
= 61.53539113... to 73.82824523...
are the values within one standard deviation of the mean. You can either use a statistical software
package or rank the sample in order to count the number of sample points between these bounds.
You should find that there are 76 scores within one standard deviation of the mean. Therefore, the
proportion of scores within one standard deviation of the mean is:
76
= 0.69090909...
110
= 0.69 Rounded as last step
Similarly, the scores within two standard deviations from the mean are all those within the range
x ± 2s = 67.68181818... ± 2×6.14642705...
= 55.38896408... to 79.97467228...
, You should find that there are 104 sample values within two standard deviations of the mean.
Therefore, the proportion of scores within two standard deviations of the mean is:
104
= 0.94545455...
110
= 0.95 Rounded as last step
c) There are 67 scores less than 70. Therefore, the proportion of scores less than 70 is:
67
= 0.60909091...
110
= 0.61 Rounded as last step
2 of 20 ID: MST.DCP.ND.02.0020 [1 point]
A class of school students have completed an assignment that is marked out of 10. The teacher records the
scores and creates the following histogram based on these scores.
Select the incorrect statement based on this histogram:
Exactly 10% of students scored 6
The number of people that scored 5 is less than the number of people that scored 6
The most common score was 7
The number of people that scored 9 is less than the number of people that scored 8
Feedback [1 out of 1]
You are correct.
Discussion
A histogram is a visual aid used to present numerical data. It is analogous to the bar chart, which is
used for categorical data. When given a set of numerical data the values are placed along the
horizontal axis of a graph and a vertical bar is drawn above each value, with the height of each bar
determined by the frequency of that value in the data set.
The visual nature of a histogram allows for quick inferences to be made about the data. In this
question, the bar above the score of 7 is the tallest and therefore the score of 7 has the largest
This attempt will impact your course
performance
Homework: Summary statistics,Normal
distribution [now finished]
Total score: 42 out of 44, 95%
You have finished the assignment. Your result is recorded on our database.
Please review your feedback below. When you are ready, click home to be returned to
your eworkbook home page.
1 of 20 ID: MST.CPD.ND.09.0010c.abe [5 points]
A group of 110 students sat an aptitude test, their resulting scores are presented:
Scores: Download the data
65 67 71 63 68 68 59 66 65 74
66 65 70 68 66 70 72 58 73 64
73 64 68 73 68 75 66 68 69 65
75 74 74 69 69 70 74 59 62 71
77 83 76 79 68 58 74 73 64 75
64 79 70 56 70 54 68 53 72 69
67 54 67 70 55 67 57 76 82 59
60 68 72 62 64 72 68 58 67 79
70 70 70 65 62 64 67 62 71 66
63 60 72 70 69 60 60 69 64 72
71 64 68 72 79 68 65 77 63 62
a) Calculate the mean and standard deviation for the sample. Give your answers to 2 decimal places.
sample mean = 67.68
sample standard deviation = 6.12
b) Find the proportion of scores that are within 1 standard deviation of the sample mean and also the
proportion that are within 2 standard deviations of the sample mean. Use the unrounded values for the
mean and standard deviation when doing this calculation. Give your answers as decimals to 2 decimal
places.
Proportion of scores within 1 standard deviation of the mean = 0.69
Proportion of scores within 2 standard deviations of the mean = 0.95
c) Find the proportion of values in the sample that are less than 70. Give you answer as a decimal to 2
decimal places.
, Proportion of values less than 70 = 0.61
Feedback [5 out of 5]
a) You are correct.
b) You are correct.
c) You are correct.
Discussion
a) Using a statistical software package, the following results can be obtained:
Sample Statistics
sample mean 67.68181818...
sample standard deviation 6.14642705...
Alternatively, the sample mean and standard deviation statistic can be calculated using the
following formulas: show variables
x =
∑xi
n
= 67.68181818...
= 67.68 Rounded as last step
∑ (xi x)2
s2 =
n1
s = 6.14642705...
= 6.15 Rounded as last step
b) From the results in part a) you can now determine that all values within
x ± s = 67.68181818... ± 6.14642705...
= 61.53539113... to 73.82824523...
are the values within one standard deviation of the mean. You can either use a statistical software
package or rank the sample in order to count the number of sample points between these bounds.
You should find that there are 76 scores within one standard deviation of the mean. Therefore, the
proportion of scores within one standard deviation of the mean is:
76
= 0.69090909...
110
= 0.69 Rounded as last step
Similarly, the scores within two standard deviations from the mean are all those within the range
x ± 2s = 67.68181818... ± 2×6.14642705...
= 55.38896408... to 79.97467228...
, You should find that there are 104 sample values within two standard deviations of the mean.
Therefore, the proportion of scores within two standard deviations of the mean is:
104
= 0.94545455...
110
= 0.95 Rounded as last step
c) There are 67 scores less than 70. Therefore, the proportion of scores less than 70 is:
67
= 0.60909091...
110
= 0.61 Rounded as last step
2 of 20 ID: MST.DCP.ND.02.0020 [1 point]
A class of school students have completed an assignment that is marked out of 10. The teacher records the
scores and creates the following histogram based on these scores.
Select the incorrect statement based on this histogram:
Exactly 10% of students scored 6
The number of people that scored 5 is less than the number of people that scored 6
The most common score was 7
The number of people that scored 9 is less than the number of people that scored 8
Feedback [1 out of 1]
You are correct.
Discussion
A histogram is a visual aid used to present numerical data. It is analogous to the bar chart, which is
used for categorical data. When given a set of numerical data the values are placed along the
horizontal axis of a graph and a vertical bar is drawn above each value, with the height of each bar
determined by the frequency of that value in the data set.
The visual nature of a histogram allows for quick inferences to be made about the data. In this
question, the bar above the score of 7 is the tallest and therefore the score of 7 has the largest
