Part B Hypothesis Testing & Confidence Intervals

Running Head: DATA ANALYSIS

DATA ANALYSIS 2

DATA ANALYSIS

Name

Institute of Affiliation

Date

Introduction

This exercise covers a variety of statistic analysis method on a number of variables; sales, calls, time, year and type. For each of the above, where applicable, mean, mode, median, minimum, maximum, upper and lower quartile ranges have been evaluated and presented on a table. There are graphic representations of each of the five variables where most of variables were suitable for a histogram whiles others were suited for pie chart. A number of variables has been paired, sales & calls, sales & time, and sales & years, and their relationship observed by use of graphs. While some of them show linear relationships, others only indicate quadratic relationship.

Analysis

Sales

The five-number summary is as follows;

min	21
maximum	54
Q1	41.25
median	44
q3	47
mean	43.35
mode	46

The minimum sales made during the week was 21 and the maximum number of sales was 54 while the average number of sales was 46. For that week, 46 sales were made frequently by the sales person. 44 represent the middle value of sales made during the week. The lower quarter sales made during the week was 41.25 and the upper quarter of sales made during the week was 47. Below is the histogram and frequency table;

Table 1: Frequency table

Class interval	Frequency
26	1
31	2
36	10
41	11
46	48
51	23
56	4
More	0

From the histogram, the highest number of sales made were between 41- 46.

The number of calls

min	116
maximum	198
Q1	146
median	157.5
q3	173.75
mean	158.86
mode	146

The least calls made during the week were 116 while the highest calls made were 198. The median calls was 157.5 while the average number of calls was 158.86. 146 was the median calls marked the lower quarter of calls made and the upper quartile was 173.75. below is the histogram .

The class interval with the highest frequency was 145-160 followed by 160 -170 with frequencies as 34 and 27 respectively.

Times

The summary of analysis of the average time per call is as follows;

min	10
maximum	22
Q1	13.2
median	15.35
q3	17.65
mean	15.531
mode	13.2

The least time per call was 10 and the maximum time per call was 22. Average time per call was 15.53 and most calls took a time of 13.2 . the upper quartile was 17.65 per call and lower quartile range was 13.2. below is a histogram .

The highest number of calls took time between 14-18.

Years

The mean, mode, median, minimum, maximum, upper and lower quartile ranges have been evaluated and presented on the table below.

min	0
maximum	5
Q1	1
median	2
q3	3
mean	2.22
mode	3

From the table above, the minimum years of experience is 0 while the maximum years of experience is 5. The mean value of the years of experience is 2.22 years while most people have 3 years of experience. 1 is the value of the lower quartile range and 3 is the value of the upper quartile range.

Below is the histogram for the number of years of experience.

The 2.85-3.8 class has the highest frequency value of 28 followed closely by 1.9- 2.85 class which has a frequency value of 26. The 4.75 -5.7 class has the lowest frequency with a value of 4.

Type

The nature of the data does not allow the evaluation of the mean, mode, median, minimum, maximum, upper and lower quartile range like it was with other variables. However, a pie chart was used to represent the data visually.

There are three types of sales outlet, online, group and none. Online takes the lion share with about 46% while none takes only 13% of the total number. Group has 41% of the total.

Pairing

1. Sales and calls pair.

Below is a graph of sales against the number of calls

Figure 1: sales against the number of calls

Sales and calls appear to have a linear relationship after modelling it where the gradient is 0.2803. since the gradient is positive, it means as number of calls increase, the sales increases by a factor of 0.2803. The R square value is 0.699 and it means that there is a 69.9% probability of changes in sale volume with the change in number of calls.

Sales and time of call

Sales against average time of call is as follows;

Figure 2: Sales against average time of call

There is a positive correlation between the number od sales and the average time of a call. From the graph, the equation has a positive gradient ( 0.1734). this means that when the calls time increases, there is a probability of 65.79% that the sales will also increase.

Sales and years of experience

The graph of sales against the years of experience appears as follows;

Figure 3: sales against years of experience

From the above figure, the number of sales increases with the years of experience up 3.8 years and then it starts to decline steadily.

Conclusion

The number of sales appear to a linear and positive correlations with the number of calls and the amount of time that each call took. However, years of experience and sales have a quadratic relationship where as the number of years of experience increase so does the sales up to a certain point where it starts to decrease.

References

Srivastava, T. N., & Rego, S. (2018). Statistics for management.

Folks, L. (2011). Ideas of statistics. New York: Wiley.

Histogram

Frequency 10 14 18 22 More 1 31 47 20 0

class interval

Frequency

Type

online group none 46 41 13

sales against calls

Sales (Y)

116 116 118 125 129 131 131 131 132 135 136 136 137 139 140 140 141 142 143 143 146 146 146 146 146 146 147 147 148 149 149 149 150 150 150 151 151 151 152 152 153 153 154 154 154 155 156 156 157 157 158 158 159 160 161 162 162 163 164 165 165 165 166 167 167 167 167 168 168 169 170 171 171 172 173 174 175 175 175 175 175 177 178 179 180 181 181 182 183 183 185 185 186 186 188 189 190 191 195 198 21 21 31 33 32 29 33 42 40 33 33 41 45 42 33 41 42 42 35 40 32 34 40 43 44 45 41 42 42 40 41 43 32 43 46 41 43 44 43 44 43 46 40 41 43 43 42 43 45 46 44 44 42 48 46 46 47 43 45 44 44 44 45 45 46 46 46 48 48 46 48 45 47 45 50 49 45 47 50 51 54 44 48 50 46 49 51 51 47 50 47 50 46 49 53 46 52 49 54 51

calls

Sales

Sales against average time

Sales (Y)

19.9 18.0 19.4 16.9 18.5 14.6 10.0 19.4 18.5 15.3 16.9 19.3 15.7 12.4 17.5 13.9 12.2 17.0 17.7 18.3 15.4 15.8 18.2 16.4 16.5 15.6 18.5 13.2 10.5 14.2 13.2 12.7 19.4 17.4 20.7 18.0 14.3 15.2 17.2 16.0 13.2 22.0 16.4 14.5 15.3 11.2 18.6 20.5 16.3 19.3 13.9 11.8 13.6 15.8 13.2 15.7 16.4 11.7 17.2 17.4 15.0 19.2 19.5 14.5 10.1 14.8 15.8 12.3 15.9 14.8 12.1 19.4 17.3 12.6 13.3 18.3 18.3 13.9 15.1 12.0 14.2 15.3 12.6 12.8 15.1 12.4 11.4 17.9 13.0 11.7 15.2 16.4 14.1 17.5 11.0 20.0 13.2 13.1 15.2 13.0 10 22 13.2 15.35 17.65 15.531 13.2 class interval 10 14 18 22 21 21 31 33 32 29 33 42 40 33 33 41 45 42 33 41 42 42 35 40 32 34 40 43 44 45 41 42 42 40 41 43 32 43 46 41 43 44 43 44 43 46 40 41 43 43 42 43 45 46 44 44 42 48 46 46 47 43 45 44 44 44 45 45 46 46 46 48 48 46 48 45 47 45 50 49 45 47 50 51 54 44 48 50 46 49 51 51 47 50 47 50 46 49 53 46 52 49 54 51

time

sales

Histogram

Frequency 26 31 36 41 46 51 56 More 1 2 10 11 48 23 4 0

21

Frequency

Histogram

Frequency 110 130 145 160 175 190 205 More 0 4 15 34 27 16 3 0

class interval

Frequency