Question

Content Course Home Support Portal Communication Assessment Assignments The marks for Dr. Smiths?s third-year classes in zoology are given below: ClassA 171182155|76 160171 190184|95|64171 170173|45 73|51168 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) ? (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

I used R software to solve this problem.

R code:

> class_A=c(71,82,55,76,66,71,90,84,95,64,71,70,73,45,73,51,68)
> length(class_A)
[1] 17
> class_B=c(54,80,12,61,73,69,92,81,80,61,75,74,15,44,91,63,50,84)
> length(class_B)
[1] 18
> summary(class_A)
Min. 1st Qu. Median Mean 3rd Qu. Max.
45.00 66.00 71.00 70.88 76.00 95.00
> table(class_A)
class_A
45 51 55 64 66 68 70 71 73 76 82 84 90 95
1 1 1 1 1 1 1 3 2 1 1 1 1 1
> summary(class_B)
Min. 1st Qu. Median Mean 3rd Qu. Max.
12.00 55.75 71.00 64.39 80.00 92.00
> table(class_B)
class_B
12 15 44 50 54 61 63 69 73 74 75 80 81 84 91 92
1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1

1. Measure of central tendency are as follows,

For class A

mean = 70.88 median= 71 mode= 71

For class B

Mean = 64.39 median= 71 mode = 61 and 80

2. Variance and standard deviation:

> v1= var(class_A)*16/17

[1] 157.3979
> sd1=sqrt(v1)
> sd1
[1] 12.54583
> v2=var(class_B)*17/18

[1] 492.1265
> sd2=sqrt(v2)
> sd2
[1] 22.18393
  

For class A:

Variance =  157.3979 and standard deviation = 12.54583

For class B:

Variance =  492.1265 and standard deviation = 22.18393

3. Five figure summary

> summary(class_A)
Min. 1st Qu. Median Mean 3rd Qu. Max.
45.00 66.00 71.00 70.88 76.00 95.00

> summary(class_B)
Min. 1st Qu. Median Mean 3rd Qu. Max.
12.00 55.75 71.00 64.39 80.00 92.00

Inter-quartile range,

For Class A, IQR= Q₃ - Q₁ = 76 - 66 = 10

for class B IQR= Q₃ - Q₁ = 80-55.75= 24.25

4.

> boxplot(class_A)

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> boxplot(class_B)

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5.

From box plot and summary statistic we see that,

class A students marks are symmetrically distributed while Class B students marks are negatively skewed.