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80 students scores recorded 68 84 75 82 68 90 62 88 76 93 73 88 73 58 93 71 59 58 5161 65 75 87 74 62 95 78 63 72 66 96 79 65 74 77 95 85 78 8671 78 78 62 80 67 69 83 76 62 71 75 82 89 67 58 73 74 73 6581 76 72 75 92 97 57 63 83 81 82 53 85 94 52 78 88 77 71mean exam score

Sagot :

Solution

We have the following values:

68,84,75,82,68,90,62,88,76,93,73,79,88,73,58,93,71,59,

58,51,61,65,75,87,74,62,95,78,63,72,66,96,79,65,74,77,95,

85,78,86,71,78,78,62,80,67,69,83,76,62,71,75,82,89,67,58,

73,74,73,65,81,76,72,75,92,97,57,63,68,83,81,82,53,85,94,

52,78,88,77,71

Part a

Range = Max- Min= 97-51= 46

Part b

The mean is given by:

[tex]\text{Mean}=\frac{\sum ^n_{i\mathop=1}x_i}{n}=75[/tex]

Part c

The median is given by:

Position 40 ordered= 75 and Position 41 ordered= 75

Then the median is:

[tex]\text{Median}=\frac{75+75}{2}=75[/tex]

Part d

The most is the most frequent value and for this case is:

Repeated 5 times

Mode = 78

Part e

The data within the interval 50-54 is:

51 52 53

The variance is given by:

[tex]s^2=\frac{\sum ^n_{i\mathop=1}(x_i-Mean)^2}{n-1}=1[/tex]

And the deviation si:

[tex]s=\sqrt[]{1}=1[/tex]

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