Victor Vincent Renner

Student ID: D40407205In partial fulfillment of the requirements for

MATH 533 Applied Managerial Statistics

Course Project Part IKeller Graduate School of Management

Professor Panakkal Mathew November 2015

Table of Content Page1.0 Introduction..

4a) Descriptive vs Continuous Variables

4b) Clarification between descript and continuous variables .

42.0 Analysis of individual variables.

52.1Salesa) Descriptive statistics using mini-tab

5b) Stem and leaf display sale

6c) Summary..

6

2.2Calls

a) Descriptive statistics using mini-tab.

7b) Boxplot..

7c) Summary...

72.3Time

a) Descriptive statistics using mini-tab.

7

b)Histogram..

8

c) Summary

83.0Analysis of selected variables pairs

3.1Sale vs Calls..

8

a)Descriptive statistics Sale vs Calls using mini-tab

8

b) Graph..

8

c)Summary.83.2Sale vs Year

a)Stem and leaf display on year and sale.9

b)Graph9

c) Summary103.3 Type and Sale

a) Graph and Summary..103.4Calls vs Time

a)Descriptive statistics on Calls and Time.11

b)Graph11

c)Summary..113.5Calls vs Year

a)Descriptive statistics Sale vs Calls using mini-tab..12

b) Chart.12

c) Summary..123.6Calls vs Type

a) Bar Chart and summary133.7Time and Year

a)Descriptive statistics on Time and Year15

b)Graph.153.8Time and Type

a)Graph..15

b) Summary.153.9Years vs Type

1.0Introduction

What are Variables? A variable is an attribute that describes a person, place. Thing or idea and the value of a variable can vary from one entity to another.

For instance. A persons hair color is a potential variable, which could have the value of blond for one person and brunette for another.

Quantitative vs. Qualitative VariablesVariables can be classified as qualitative (categorical) or quantitative (numeric).

Qualitative variables take on values that are names or labels. The color of a ball (e.g., red,

green, blue) or the breed of a dog (e.g., collie, shepherd, and terrier) would be examples

of qualitative or categorical variables. Quantitative. Quantitative variables are numeric. They represent a measurable quantity. For example, when we speak of the population of a city, we are talking about the number of people in the city - a measurable attribute of the city. Therefore, population would be a quantitative variable.

In algebraic equations, quantitative variables are denoted by symbols (e.g.,x,y, orz).a) Discrete vs. Continuous VariablesQuantitative variables can be further classify as discrete or continuous. If a variable take a value between its minimum value and its maximum value, it will be consider as a continuous variable: otherwise, called a discrete variable.

b) Clarification between Discrete and Continuous Variable Suppose the fire department mandates that all fire fighters must weigh between 150 and 250 pounds. The weight of a fire fighter would be an example of a continuous variable; since a fire fighter's weight could take on any value between 150 and 250 pounds.

Suppose we flip a coin and count the number of heads. The number of heads could be any integer value between 0 and plus infinity. However, it could not be any number between 0 and plus infinity. We will not get 2.3 heads. Therefore, the number of heads must be a discrete variable.Statistical data are classify according to the number of variables studied.

Univariate data. When we conduct a study that looks at only one variable, we say that we are working with univariate data. Suppose, for example, that we conducted a survey to estimate the average weight of high school students. Since we are only working with one variable (weight), we would be working with univariate data.

Bivariate data. When we conduct a study that examines the relationship between two variables, we are working with bivariate data. Suppose we conducted a study to see if there were a relationship between the height and weight of high school students. Since we are working with two variables (height and weight), we would be working with bivariate data.2.0Analysis of Individual Variables

2.1SALES

Calculating the mean and median on sale using mini-tab.

a) Descriptive Statistics: SALES

Variable N N* Mean SE Mean StDev CoefVar Minimum Q1 Median

SALES 96 0 42.385 0.428 4.191 9.89 32.000 40.000 42.000

Variable Q3 Maximum Skewness

SALES 45.000 52.000 0.06

b) Graph

Stem-and-Leaf Display: SALES

Stem-and-leaf of SALES N = 96

Leaf Unit = 1.0

2 3 23

4 3 45

13 3 677777777

23 3 8888899999

41 4 000000001111111111

(17) 4 22222222233333333

38 4 44444444444455555

21 4 66667777

13 4 888889999

4 5 01

2 5 22

A. The number of observation is 96.

B. At the bottom of the stem and leaf, the stem is 2 and the leaves are 5, 2, 2. The numbers in the original data set are 5, 2, 2.

c) SummaryIn the above calculations on mean and median, the mean is calculated as the sum total of sale divided by the amount of rows in the given data set. Using Mini-tab the speculated mean is 42.385. The can be calculated or arrived as the middle number of the given figure figures in the set after re-arranging the set of number from ascending or descending order. It has a formula denoted as (N+1) divided by 2. Using Mini-tab in calculating the median our answer is 42.000.

2.2CALLSa) Calculations Calculating the mean, median first quartile third quartile and the skewness on calls using mini-tab.

Descriptive Statistics: CALLS

Variable Mean Q1 Median Q3 Skewness

CALLS 162.29 149.25 160.50 177.75 0.02

b) Boxplot of Calls

c) SummaryUsing Mini-tab in calculating the mean for the number of sale calls made this week is 162.29 and the median is 160.50. From the above boxplot, the first quartile is 149.25 the third quartile is 177.75 and the data concerning the number of sale calls made this week skewed to the right. 2.3TIME Calculating the mean and median on sale using mini-tab.a) Descriptive Statistics: TIME

Variable N N* Mean SE Mean StDev CoefVar Minimum Q1 Median Q3

TIME 97 0 30.4 15.0 148.1 487.38 10.0 13.5 15.1 17.1

Variable Maximum Skewness

TIME 1474.2 9.84

The mean is 30.4, standard deviation of 148.1, first quartile is 13.5, median is 15.1, third quartile is 17.1 skewness is positive.b) Graph

From the histogram the highest frequency of time is approximately 18 with a time of 15, the lowest frequency is 2 with a time of 10, 21 and 223.0

Analysis of selected variable pair

3.1Sale vs Callsa) Descriptive Statistics: SALES, CALLS

Variable Mean StDev Q1 Median Q3

SALES 42.385 4.191 40.000 42.000 45.000

CALLS 162.29 18.17 149.25 160.50 177.75

b) Charts

c) Sale vs Calls SummaryFrom the above datas the variable values for calls exceeded that of the variables values of sale. According to the above pie chart out off 100 %, 21% goes to sale and it is in the blue sector, 78% went to Calls and it is in the brown sector of the pie chart.On the histogram on sales, we have 11 bars and that of time we have 12 bars. On sake histogram the bar with sale 44 has a frequency of approximately 18 and on the histogram on time at 15, the frequency is approximately 18. The size of the bars on the two histograms sales and time vary in size.

3.2Sale and Yeara) Descriptive Statistics: YEARS, SALES

Variable N N* Mean SE Mean StDev CoefVar Minimum Q1 Median

YEARS 97 0 3.98 1.97 19.43 488.21 0.00 1.00 2.00

SALES 96 0 42.385 0.428 4.191 9.89 32.000 40.000 42.000

Variable Q3 Maximum Skewness

YEARS 3.00 193.00 9.79

SALES 45.000 52.000 0.06

b) Stem-and-Leaf Display: SALES, YEARS

Stem-and-leaf of SALES N = 96

Leaf Unit = 1.0

2 3 23

4 3 45

13 3 677777777

23 3 8888899999

41 4 000000001111111111

(17) 4 22222222233333333

38 4 44444444444455555

21 4 66667777

13 4 888889999

4 5 01

2 5 22

Stem-and-leaf of YEARS N = 96

Leaf Unit = 0.10

10 0 0000000000

33 1 00000000000000000000000

(31) 2 0000000000000000000000000000000

32 3 000000000000000000000

11 4 0000000000

1 5 0

c) Sale and Year summary

With my comparison on sale and year with reference to stem and leaves graph. Both variables have a total of N=96 with differences in the leaves unit, with the sale variables the leaf unit =1.0 and that of the year the leaf unit is 0.10. On the sale I have eleven (11) rolls and that of the year I have six (6) rolls, with the year variables on the stem and leaf graph I have more numerical values with zeros (0) and on the sale I have numerical values with approximately ten (10) zeros.3.3Type and Sale chart

a) Summary on Type and SaleWith the pie chart on Type, the chart is sub divided into three sector concerning the type of variables contain in the giving data. Online has 51.0% with a blue sector, Group has 30.3% with a brown sector and none has 18.8 %with green sector. The sector are clearly visible and spacious. With Pie chart on sale, it has about twenty-one (21) sectors and most of the sectors are very compact together.3.4Calls vs Timea) Descriptive Statistics Variable Mean St Dev Minimum Q1 Median Q3 Maximum IQR

CALLS 162.29 18.17 124.00 149.25 160.50 177.75 201.00 28.50

TIME 15.356 2.435 10.000 13.500 15.050 17.000 21.600 3.500

N for

Variable Mode Mode Skewness

CALLS 149 6 0.02

TIME 14.6, 14.8 4 0.28

From the above calculations on calls vs time, there are larger difference between the mean for both variables for instance, the calls variable has a mean of 162.29 and the time variable has a mean of 15.356. Generally, there are vast differences between the two variables with calls variable having the highest values and time variable with low values. b) Graph Pie chart Calls and Time

From the above pie chart, the blue sector with label 1, consist of calls variables having 91% and the brown sector label 2 consisting with Time variables with 9%. According to the pie chart, more calls made within a very small percentage period.3.5Calls and Year

a) Descriptive Statistics: CALLS, YEARS

Variable N N* Mean SE Mean St De Minimum Q1 Median Q3 Maximum

CALLS 97 0 321 159 1566 124 150 161 178 15580

YEARS 97 0 3.98 1.97 19.43 0.00 1.00 2.00 3.00 193.00

Variable IQR Skewness

CALLS 29 9.85

YEARS 2.00 9.79

The above calculation for variables calls and years were the mean, standard deviation, minimum and maximum values, first quartile median third quartile, the semi-interquartile range and the skewness values. b) Graphs From the histogram of calls and Year, I have sixteen bars for Calls and a highest frequency of 13. The histogram of year has six (6) bars with a highest frequency of approximately 30. On the Calls histogram I have a mean of 162.3, standard deviation of 18.7 and that of year I have a mean of 2.010 and a standard deviation of 1.152.

3.6Calls vs TypeThere are no mathematical calculation on call and type because they have different variables namely qualitative and quantitative variables.

On the pic chart with type and calls, the sectors has various differences. The type pie chart has three sectors and they are qualitative. The call pie chart has numerous sectors and they are quantitative and has extra added colors and they are compact arranged.

3.7Time and Yeara) Descriptive Statistics: TIME, YEARS

Variable N N* Mean SE Mean St Dev Variance Sum Q1 Median

TIME 96 0 15.356 0.248 2.435 5.927 1474.200 13.500 15.050

YEARS 96 0 2.010 0.121 1.183 1.400 193.000 1.000 2.000

Variable Q3 IQR Skewness

TIME 17.000 3.500 0.28

YEARS 3.000 2.000 0.14

b) Box Plot

From the above graphs for both time and Year the sum totals are 1474.200 for time and 193.000 for year, both skewness and positive. At the top of the descriptive statistics, the various calculations were achieve using mini-tab.3.8Time vs Type a) Bar Chart

b) SummaryA close look at the two Bar chart for time and type, the blocks and partially the same but differ in their numerical values. Both charts are divided into three bars, variables of time is in hundreds, and that of type is in tenths. 3.9 Year vs type These two variables has nothing in common.15

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1474.2

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