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]