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
5 | 5 6 9 |
6 | 2 3 4 4 4 9 |
7 | 7 7 |
8 | 5 |
59 + 56 + 64 + 85 + 64 + 62 + 63 + 69 + 77 + 64 + 77 + 55 = 795/12= 66.25
Mean retirement years is 66 years
Question 3
- Mean
27 + 30 + 21 + 62 + 28 + 18 + 23 + 22 + 26 + 28 =285/10 =28.5
The mean = 28.5
- Median
lies between 26 and 27
26 + 27 = 53/2
26.5
iii. Mode
The mode of the numbers is 28
- Mean
- 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
- Complete the table
No of books | Frequency |
1 – 2 | 4 |
3 – 4 | 5 |
5 – 6 | 8 |
7 – 8 | 2 |
9 – 10 | 4 |
- 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
- Median = 5
Question 6
- Mean
2 + 5 + 3 + 10 + 0 + 4 + 2 =26/7
= 3.71
- Median
0, 2, 2, 3, 4, 5, 10
= 3
iii. Mode = 2
- Median
- Median will be 2.5, mean will shift to 2.6, and the mode will remain to be 2
- 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
- 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
- The median is the best representation of this dataset. Most of the sales revolve around the median.
- 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
- A = 93
B = 87
C = 83
D = 73
E = 55
Question 10
- Median
55, 64, 73, 79, 81, 85, 86, 87, 90, 93
Median = 81 + 85 = 166/2
83
- 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
- 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.