Module 2 – Case

Student’s Name

Professor’s Name

Course

Date

Module 2 – Case

Question 1

A central tendency statistic is a quantitative metric that describes the central position or default value of a dataset. Such acts show where most values fall in the distribution and are often called the central distribution position. Mean is the average of a dataset. Median is the value in the middle of a data set. The mode is the most repeated in a dataset.

Question 2

55   77   64   77   69   63   62   64   85   64   56   59

59 + 56 + 64 + 85 + 64 + 62 + 63 + 69 + 77 + 64 + 77 + 55 = 795/12= 66.25

Mean retirement years is 66 years

Question 3

1. Mean

27 + 30 + 21 + 62 + 28 + 18 + 23 + 22 + 26 + 28 =285/10 =28.5

The mean =  28.5

1. Median

lies between 26 and 27

26 + 27 = 53/2

26.5

iii. Mode

The mode of the numbers is 28

1. Mean
2. The outlier in distribution is 62. A figure greater than 1.5 times the box’s length from the lower or upper quartiles.

Question 4

Let the final test be X

To get the least marks for x we will take:

(X + 68 + 74 + 84 + 79)/5 75

X = (5 * 75)/305

X = 70%

Question 5

1. Complete the table

1. Raw data mean

10 + 4 + 7 + 6 + 3 + 5 + 6 + 2 + 6 + 5 + 3 + 7 + 2 + 10 + 9 + 6 + 2 + 5 + 3 + 9 + 1 + 6 + 3

= 120/23  = 5.21

1. Median = 5

Question 6

1. Mean

2 + 5 + 3 + 10 + 0 + 4 + 2 =26/7

= 3.71

1. Median

0, 2, 2, 3, 4, 5, 10

= 3

iii. Mode = 2

1. Median
2. Median will be 2.5, mean will shift to 2.6, and the mode will remain to be 2
3. Mean is the most affected outliers than the mode and or the median.it can shift the mean either to be too small or to be too large.

Question 7

1. Mean

45,000*1 + 25, 000*2 + 23, 000*5 + 20, 000*4 + 15,000*3 = 335000/15

22333.33

= $22, 000

Median

15,000, 15000,15000,20000,20000,20000,20000,23000, 23000,23000,23000,23000,25000,25000,45000

$23,000

1. The median is the best representation of this dataset. Most of the sales revolve around the median.
2. Outlier of the data is 45, it shift the mean to a higher value

Question 8

A =least value in a dataset,

B = lower Quantile

C = Median

D = higher quantile

E = largest value in dataset

Question 9

2. A = 93

B = 87

C = 83

D = 73

E = 55

Question 10

1. Median

55, 64, 73, 79, 81, 85, 86, 87, 90, 93

Median = 81 + 85 = 166/2

83

1. Range

Range = largest value – least value

93 – 55 = 38

Range = 38

(55, 64, 73, 79, 81) (85, 86, 87, 90, 93)

73                                         87

87 – 73 = 14

Interquartile = 14

1. Plotting the graph of the data set, you can obtain the mean, range, both the lower and upper quantile, and the maximum value without referring to the dataset. There is a large deviation between the upper side of the plot and the lower side of the plot.