Question

Course Home Support Portal ation Assessment Content Assignments The marks for Dr. Smiths?s third-year classes in zoology are given below Class A 71 82 55 76 66 71 90 84 95 64 71 70 73 45 73 51 68 Class B 54 80 12 61 73 69 92 81 80 61 75 74 15 44 91 63 50 84 1. Determine the three measures of central tendency 2 Calculate the variance and standard deviation 3 Determine the five figure summary and the interquartile range. 4 Create a box plot for each class 5 Use the measures calculated in questions (1) 2 (3) and the box-and-whisker plot from (4) to compare the performance of the two classes. 6 Comment on the effect of outliers on these numerical summaries Rubric

Answer 1

1)

for class A

mean =    ΣX/n =    70.882

Median=0.5(n+1)th value =    9   th value of sorted data
=   71.0000  

mode=   71  

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for class B

mean =    ΣX/n =    64.389

Median=0.5(n+1)th value =    9.5   th value of sorted data
=   71.0000  

mode=   80

2)

for class A

X	(X - X̄)²
71	0.014
82	123.602
55	252.249
76	26.190
66	23.837
71	0.014
90	365.484
84	172.1
95	581.661
64	47.367
71	0.014
70	0.779
73	4.484
45	669.90
73	4.484
51	395.308
68	8.308

	X	(X - X̄)²
total sum	1205	2675.765
n	17	17

sample variance =    Σ(X - X̄)²/(n-1)=   167.2353
      
sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   12.9319

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for class B

X	(X - X̄)²
54	107.929
80	243.707
12	2744.596
61	11.485
73	74.151
69	21.262
92	762.373
81	275.9
80	243.707
61	11.485
75	112.596
74	92.373
15	2439.262
44	415.71
91	708.151
63	1.929
50	207.040
84	384.596

	X	(X - X̄)²
total sum	1159	8858.278
n	18	18

sample variance =    Σ(X - X̄)²/(n-1)=   521.0752
      
sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   22.8271

3)

for class A

quartile , Q1 = 0.25(n+1)th value=   4.5   th value of sorted data
=   65  
      
Quartile , Q3 = 0.75(n+1)th value=   13.5   th value of sorted data
=   79  

maximum =    95
minimum=   45

five number summary for class A is 45,65,71,79,95

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for class B

Median=0.5(n+1)th value =    9.5   th value of sorted data
=   71.0000  
      
quartile , Q1 = 0.25(n+1)th value=   4.75   th value of sorted data
=   53  
      
Quartile , Q3 = 0.75(n+1)th value=   14.25   th value of sorted data
=   80.25  
      
IQR = Q3-Q1 =    27.25  
five number summary is 15,53,71,80.25,92

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4)

Box plot class Alass B 90 80 70 60 50 40 30 20 10 0