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.

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