QUANT homework

Introduction

Numerical Summaries: summarize the data set

Parameters : calculated using population data

Statistics: calculated using sample data

with a well defined random sample, can be used to estimate the population parameter

Examples:

1 variable numerical summaries

measures of the center (mean, median, mode)

Measures of spread (variance, standard deviation, range, IQR, standard error)

Skewness: how symmetric is the distribution? (perfect symmetric then skewness = 0)

positive (right skewed)

negative (left skewed)

Kurtosis: how much probability is in the tails of the distirbution?

usually compares to Normal distirbution tails (kurtosis = 3)

Skewed distributions

Kurtosis

2 variable numerical summaries (will get to these later)

correlation

coefficient of determination

Numerical summaries of relative position of data values

z-scores

percentiles

Symbols

Descriptive Statistics

Can use Data Analysis Toolpak in Excel (File … Options … Data Analysis Toolpack … Go)
		Data … Data Analysis…Descriptive Statistics
	Age
	80
	91				Age
	77
	85				Mean	79.1046728209
	71				Standard Error	0.9521947114
	89				Median	79.2189722038
	82				Mode	ERROR:#N/A
	79				Standard Deviation	9.5694384163
	74				Sample Variance	91.5741516027
	68				Kurtosis	0.0747918953
	103				Skewness	0.2033261591
	92				Range	47.803631584
	85				Minimum	55.4111721156
	81				Maximum	103.2148036997
	82				Sum	7989.5719549096
	64				Count	101
	81
	84
	100
	86
	83
	67
	84
	78
	63
	70
	85
	99
	93
	79
	88
	69
	86
	103
	85
	73
	61
	71
	89
	98
	71
	81
	83
	81
	69
	65
	77
	82
	80
	78
	60
	71
	71
	73
	86
	84
	79
	77
	85
	72
	83
	89
	85
	91
	73
	76
	87
	73
	86
	85
	78
	94
	79
	76
	79
	76
	64
	78
	65
	71
	72
	68
	81
	84
	77
	68
	70
	82
	66
	81
	82
	79
	55
	99
	68
	74
	80
	76
	89
	69
	79

Frequency Distribution Table1

	Un-grouped Frequency Distribution Table
		Class	Frequency Dr77: Frequency: Unit counts for each class	Percent Dr77: Percent: =100*(Frequency/ Frequency Total)	Relative Frequency Dr77: Relative Frequency: = Frequency / Total Frequency	Cummulative Frequency Dr77: Cumulative Frequency: = Sum of all prior and the current Frequency
		Plastic	9	25.7142857143
		Wheat	7	20
		Insect	12	34.2857142857
		Metal	2	5.7142857143
		Liquid	5	14.2857142857
		Total Dr77: Total: Use =Sum feature in Excel	35

Additional table columns can be added beyond just the Frequency column

Percent Plastic Wheat Insect Metal Liquid 25.714285714285712 20 34.285714285714285 5.7142857142857144 14.285714285714285

z-score

Standard deviation unit distance a data value is from the mean of the distribution
You need
	mean
	standard deviation
	Age	Z-score
	80
	91
	77
	85
	71
	89
	82
	79
	74
	68
	103
	92
	85
	81
	82
	64
	81
	84
	100
	86
	83
	67
	84
	78
	63
	70
	85
	99
	93
	79
	88
	69
	86
	103
	85
	73
	61
	71
	89
	98
	71
	81
	83
	81
	69
	65
	77
	82
	80
	78
	60
	71
	71
	73
	86
	84
	79
	77
	85
	72
	83
	89
	85
	91
	73
	76
	87
	73
	86
	85
	78
	94
	79
	76
	79
	76
	64
	78
	65
	71
	72
	68
	81
	84
	77
	68
	70
	82
	66
	81
	82
	79
	55
	99
	68
	74
	80
	76
	89
	69
	79

percentile

Find the value where x% of the data values fall bellow
Use PERCENTILE in Excel
	write percentages in decimal format
	Age
	103			10th percentile		67.714681164
	103
	100			23rd percentile
	99
	99			79th percentile
	98
	94
	93
	92
	91
	91
	89
	89
	89
	89
	88
	87
	86
	86
	86
	86
	85
	85
	85
	85
	85
	85
	85
	84
	84
	84
	84
	83
	83
	83
	82
	82
	82
	82
	82
	81
	81
	81
	81
	81
	81
	80
	80
	80
	79
	79
	79
	79
	79
	79
	79
	78
	78
	78
	78
	77
	77
	77
	77
	76
	76
	76
	76
	74
	74
	73
	73
	73
	73
	72
	72
	71
	71
	71
	71
	71
	71
	70
	70
	69
	69
	69
	68
	68
	68
	68
	67
	66
	65
	65
	64
	64
	63
	61
	60
	55

SAT Subject Test Percentiles

Quartiles

Use QUARTILE in Excel
						5 Number Summary
	Age					Q1: Quartile 1	72
	80					Q2: Quartile 2 (Median)
	91					Q3: Quartile 3	85
	77					Minimum (=Min())	55
	85					Maximum (=Max())	103
	71
	89
	82					Interquartile Range (IQR) = Q3 - Q1	13
	79					range over 50% of data values
	74
	68					Use the IQR to identify outlier boundaries
	103
	92					Upper Bound = Q3 + 1.5(IQR)	105
	85					Lower Bound = Q1 - 1.5(IQR)	52
	81
	82					Question: Are there outliers in the Age dataset?
	64
	81
	84
	100
	86
	83
	67
	84
	78
	63
	70
	85
	99
	93
	79
	88
	69
	86
	103
	85
	73
	61
	71
	89
	98
	71
	81
	83
	81
	69
	65
	77
	82
	80
	78
	60
	71
	71
	73
	86
	84
	79
	77
	85
	72
	83
	89
	85
	91
	73
	76
	87
	73
	86
	85
	78
	94
	79
	76
	79
	76
	64
	78
	65
	71
	72
	68
	81
	84
	77
	68
	70
	82
	66
	81
	82
	79
	55
	99
	68
	74
	80
	76
	89
	69
	79

Select Data ... Insert ... Recommended Charts ... All Charts ...Box and Whisker

=QUARTILE(Data, quartile number)

histogram

Create a Histogram to see shape of distribution ( 2 ways to do this in Excel)													2) Use Insert Menu in excel
Age		Bin
80		60			Bin	Frequency
91		70			60	1
77		80			70	18
85		90			80	34
71		100			90	37
89		110			100	8
82					110	3
79
74
68
103
92
85
81
82
64
81
84
100
86
83
67
84
78
63
70
85
99
93
79
88
69
86
103
85
73
61
71
89
98
71
81
83
81
69
65
77
82
80
78
60
71
71
73
86
84
79
77
85
72
83
89
85
91
73
76
87
73
86
85
78
94
79
76
79
76
64
78
65
71
72
68
81
84
77
68
70
82
66
81
82
79
55
99
68
74
80
76
89
69
79

1) Data ... Data Analysis ... Histogram

Histogram

Frequency 60 70 80 90 100 110 1 18 34 37 8 3

Bin

Frequency

Upper Bound for Classes

histogram2

Use Histograms to visualize approximate shapes of data distirbutions

Other Charts 1

	Categorical
	Bar Chart
							Pie Chart				Pareto

Other Charts 2

	Quantitive
		Line Graph
									Ogive (Cumulative Frequency Polygon)
										Use Cumulative Frequency column of a frequency distribution table in Excel when graphing

To select disjoin columns in Excel, hold down your CTRL button while selecting the columns

empirical rule

								Need a bell-shaped distribution to use the Empirical Rule
Age
80		Age
91
77		Mean	79.1046728209
85		Standard Error	0.9521947114
71		Median	79.2189722038
89		Mode	ERROR:#N/A
82		Standard Deviation	9.5694384163
79		Sample Variance	91.5741516027
74		Kurtosis	0.0747918953
68		Skewness	0.2033261591				Question1: Approximately what percent of the age data is within 1 standard deviation unit of the mean?
103		Range	47.803631584								68% of the data values
92		Minimum	55.4111721156
85		Maximum	103.2148036997
81		Sum	7989.5719549096				Question2: Within what interval are approximately 68% of the age data values? (Hint: need standard deviation of the distirbution)
82		Count	101									upper bound		88.6741112372
64												lower bound		69.5352344046
81
84											Approximately 68% of the age data will fall between 69 years to 89 years
100
86
83
67
84
78
63
70
85
99
93
79
88
69
86
103
85
73
61
71
89
98
71
81
83
81
69
65
77
82
80
78
60
71
71
73
86
84
79
77
85
72
83
89
85
91
73
76
87
73
86
85
78
94
79
76
79
76
64
78
65
71
72
68
81
84
77
68
70
82
66
81
82
79
55
99
68
74
80
76
89
69
79