Question

In one of classes of Professor C, there are 25 students, one test scores are listed below 77 75 53 79 87 63 71 79 82 76 14 72 71 56 61 77 79 63 79 67 52 78 77 54 64 a) Find the mean (that is the test average). Write down the formula first. 2. b) Find the median, explain the meaning of the result c) Find the sample variance (write the expression in detail and you may use calculator)wddh monbe d) Find the sample standard deviation. Write down the formula you used and show your work.
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Answer #1
X (X - X̄)²
77 76.738
75 45.698
53 232.258
79 115.778
87 351.938
63 27.458
71 7.618
79 115.778
82 189.338
76 60.218
14 2941.978
72 14.138
71 7.618
56 149.818
61 52.418
77 76.738
79 115.778
63 27.458
79 115.778
67 1.538
52 263.738
78 95.258
77 76.738
54 202.778
64 17.978
X (X - X̄)²
total sum 1706 5382.56
n 25 25

a)

mean =    ΣX/n =    68.24
b)

median = (n+1)/2=13th term from ascending order

so, median=72

median is measure of center of data.

so, center value of data is 72

c)

sample variance =    Σ(X - X̄)²/(n-1)= 5382.56/24= 224.273

d)

sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =√224.273 = 14.9758

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