Math 216: Statistical Thinking

Descriptive Statistics

Summarize and visualize data to make sense of it.
Descriptive statistics (or exploratory data analysis (EDA)) involves summarizing and visualizing variables and their relationships.
The methods depend on the type of variable(s) being analyzed (qualitative or quantitative).

One Qualitative Variable

A random sample of US adults in 2012 were surveyed regarding the type of cell phone owned.

Android? iPhone? Blackberry? Non-smartphone? No cell phone?

Frequency Table

A frequency table shows the number of cases or counts that fall in each category:

Subset of Raw Data	Device Type
Case 1	Android
Case 2	none
Case 3	none
Case 4	iPhone
Case 5	Non Smartphone
Case 6	iPhone
Case 7	Blackberry
Case 8	Non Smartphone
Case 9	Android
Case 10	Android
…	(for 2253 cases …)

Cell Phone Type	Frequency
Android	458
iPhone	437
Blackberry	141
Non Smartphone	924
No Cell Phone	293
Total	2253

Proportion

The proportion in a category is found by: \[ \text{proportion} = \frac{\text{number in category}}{\text{total sample size}} \]

Population proportion (parameter): \(p\)
Sample proportion (statistic): \(\hat{p}\) (“p-hat”)

What proportion of adults sampled do not own a cell phone?

Cell Phone Type	Frequency	Proportion
Android	458	0.203
iPhone	437	0.194
Blackberry	141	0.063
Non Smartphone	924	0.410
No Cell Phone	293	0.130
Total	2253	1.000

Bar Chart

In a barplot, the height of the bar corresponds to the number of cases falling in each category.

Two Qualitative Variables

Look at the relationship between two qualitative variables:

Relationship status
Gender

	Female	Male	Total
In a Relationship	32	10	42
It’s Complicated	12	7	19
Single	63	45	108
Total	107	62	169

Relationship Status and Gender

Proportion of students in a relationship that are female?

prop.relation.female <- 32/42
round(prop.relation.female, 2)

[1] 0.76

Proportion of students in a relationship that are male?

prop.relation.male <- 10/42
round(prop.relation.male, 2)

[1] 0.24

Difference in Proportions

A difference in proportions is a difference in proportions for one qualitative variable calculated for different levels of the other qualitative variable.

Example: Difference in proportions of male and female that are in a relationship: \[ \hat{p}_F - \hat{p}_M = \frac{32}{107} - \frac{10}{62} = 0.14 \]

prop.female <- 32/107
prop.male <- 10/62
prop.diff <- prop.female - prop.male
round(prop.diff, 2)

[1] 0.14

Student Survey

Dataset on 362 responses to a student survey given at one college.

Year	Gender	Smoke	Exercise	TV	Height	Weight	Siblings	BirthOrder	GPA	Pulse
Senior	M	No	10.0	1	71	180	4	4	3.13	54
Sophomore	F	Yes	4.0	7	66	120	2	2	2.50	66
FirstYear	M	No	14.0	5	72	208	2	1	2.55	130
Junior	M	No	3.0	1	63	110	1	1	3.10	78
Sophomore	F	No	3.0	3	65	150	1	1	2.70	40
Sophomore	F	No	5.0	4	65	114	2	2	3.20	80
FirstYear	F	No	10.0	10	66	128	1	1	2.77	94
Sophomore	M	No	13.0	8	74	235	1	1	3.30	77
Junior	F	No	3.0	6	61	NA	2	2	2.80	60
FirstYear	F	No	12.0	1	60	115	7	8	3.70	94
Sophomore	F	No	12.0	6	65	140	1	2	2.09	63
FirstYear	M	No	10.0	5	63	200	2	2	NA	72
Sophomore	M	No	12.0	8	68	162	3	NA	2.90	54
Junior	F	No	6.0	1	68	135	2	3	3.08	66
FirstYear	M	No	9.0	5	68	193	1	1	NA	72
FirstYear	F	No	10.0	2	63	110	1	2	3.86	59
FirstYear	F	No	3.0	15	63	99	2	1	3.00	88
Sophomore	M	No	7.0	3	72	165	2	1	3.00	59
Sophomore	F	No	2.0	1	62	120	1	1	3.35	64
Sophomore	F	No	14.0	2	67	154	1	2	3.30	72
Sophomore	F	No	10.0	5	65	110	1	2	3.40	74
Sophomore	F	No	14.0	2	68	145	8	8	2.90	70
FirstYear	M	No	20.0	20	73	195	3	4	3.50	58
Sophomore	M	No	7.0	10	74	200	1	2	3.00	48
Sophomore	M	No	12.0	3	70	167	1	2	3.30	74
Sophomore	M	No	10.0	5	71	175	3	2	3.70	60
Sophomore	F	No	6.0	8	67	155	1	1	3.48	74
Junior	M	No	14.0	2	74	185	1	2	3.40	70
FirstYear	M	No	12.0	6	68	190	1	1	2.50	74
Senior	M	No	10.0	4	72	165	1	2	3.30	60
Junior	M	No	8.0	8	62	175	2	3	3.50	55
Sophomore	F	No	0.0	2	66	126	5	6	3.79	82
FirstYear	M	No	10.0	20	70	187	3	2	3.30	68
Senior	M	No	6.0	10	72	170	2	2	2.90	83
FirstYear	F	No	5.0	2	67	158	4	2	2.68	53
Sophomore	F	No	24.0	5	62	119	1	2	3.28	72
FirstYear	M	No	2.0	5	73	205	1	1	3.51	86
Sophomore	F	No	10.0	5	67	129	1	1	2.60	67
Sophomore	F	No	6.0	5	67	145	0	1	3.85	89
Junior	F	No	5.0	5	64	130	0	NA	2.40	48
Senior	M	No	5.0	5	72	215	3	1	3.40	64
Sophomore	F	No	12.0	4	64	135	2	3	2.40	73
Sophomore	F	No	2.0	5	70	145	0	1	3.00	80
FirstYear	F	No	7.0	8	60	98	2	2	3.10	85
FirstYear	M	No	15.0	2	71	150	1	1	2.94	60
Junior	M	No	5.0	14	73	159	1	1	3.31	61
Senior	M	No	7.0	20	72	174	1	2	3.30	80
Sophomore	M	No	15.0	20	74	160	1	2	2.90	70
Senior	M	No	8.0	10	70	165	1	2	3.40	61
Sophomore	F	No	14.0	3	69	161	1	2	3.16	58
FirstYear	M	No	14.0	1	68	160	2	1	NA	42
Senior	F	No	4.0	14	64	130	2	2	3.84	88
Junior	M	No	15.0	0	72	175	2	1	3.60	68
Senior	M	No	4.0	20	70	255	2	2	2.36	68
Junior	M	No	15.0	2	65	160	4	4	2.90	35
FirstYear	M	No	3.0	6	72	160	0	1	3.00	90
Junior	F	No	3.0	15	63	95	0	1	3.30	88
Sophomore	F	No	15.0	3	64	115	2	2	3.70	67
Sophomore	F	No	20.0	2	64	120	1	1	2.90	71
FirstYear	F	No	3.0	1	65	135	2	3	3.60	68
Sophomore	M	No	6.0	7	73	180	1	2	3.56	73
Senior	M	No	12.0	7	71	155	0	1	3.70	55
FirstYear	F	No	4.0	3	66	110	2	1	4.00	78
FirstYear	M	No	20.0	12	73	215	2	3	3.40	96
FirstYear	M	No	15.0	6	70	175	2	3	NA	63
Sophomore	F	No	10.0	3	65	140	3	4	3.30	73
FirstYear	M	No	10.0	20	72	195	2	2	3.10	60
Sophomore	M	No	4.0	8	73	185	2	1	2.50	80
Sophomore	M	No	9.0	0	70	185	2	1	3.20	96
Senior	M	No	12.0	12	79	209	1	1	3.10	49
Senior	F	No	2.0	6	67	145	3	2	3.50	62
Sophomore	F	No	15.0	4	66	140	1	1	3.00	68
FirstYear	F	No	10.0	4	66	146	1	2	3.25	52
FirstYear	F	No	7.0	6	68	130	2	1	2.40	71
Sophomore	F	No	3.0	5	67	140	1	2	3.22	72
FirstYear	F	No	4.0	3	66	130	1	1	NA	65
FirstYear	F	No	15.0	3	66	140	1	1	NA	90
Sophomore	F	No	8.0	8	65	160	3	3	3.64	77
Sophomore	F	No	5.0	8	66	120	1	1	3.50	68
Sophomore	M	No	10.0	20	76	150	1	1	2.50	60
Sophomore	M	No	15.0	5	69	155	1	1	3.40	65
FirstYear	F	No	4.0	4	64	128	3	1	NA	60
FirstYear	F	No	5.0	4	64	143	2	2	3.25	84
Junior	F	No	6.0	3	65	155	2	1	3.70	80
FirstYear	F	No	18.0	2	67	119	2	1	2.10	66
Sophomore	F	No	16.0	4	66	138	1	2	2.80	70
Senior	M	No	4.0	5	72	240	1	1	3.49	70
FirstYear	F	No	3.0	2	65	160	1	1	3.83	72
FirstYear	M	No	20.0	3	69	191	3	1	NA	66
FirstYear	M	No	5.0	8	69	165	5	4	2.70	69
Sophomore	M	No	10.0	6	73	200	2	3	2.80	89
FirstYear	F	No	2.0	4	62	125	1	1	3.13	79
Sophomore	F	No	4.0	5	69	140	2	3	3.62	98
Sophomore	M	No	14.0	5	73	206	1	1	2.00	48
FirstYear	M	No	7.0	5	76	275	1	2	3.60	71
Sophomore	M	No	12.0	8	70	142	1	2	4.00	51
Sophomore	F	No	14.0	2	67	140	6	7	3.10	67
Sophomore	M	No	3.0	10	68	145	5	6	2.60	66
Sophomore	M	No	5.0	4	72	128	1	1	3.70	66
FirstYear	M	No	15.0	5	74	165	1	1	3.57	60
Senior	F	No	5.0	20	62	140	1	1	2.90	77
Sophomore	F	No	4.0	14	69	130	1	2	3.15	80
FirstYear	M	No	8.0	2	70	170	3	2	3.88	70
Sophomore	M	No	14.0	4	69	160	2	2	3.50	65
Sophomore	M	No	5.0	8	72	165	2	2	2.80	57
	F	No	12.0	7	78	145	1	1	NA	37
Sophomore	M	No	15.0	5	67	155	1	2	2.90	84
Sophomore	M	No	3.0	3	73	155	3	2	3.21	56
Sophomore	F	No	12.0	1	63	113	1	2	3.50	69
Sophomore	M	No	12.0	5	70	155	1	2	3.33	62
Sophomore	M	No	6.0	20	NA	173	1	1	3.00	79
Sophomore	M	No	2.0	8	65	195	2	1	3.50	55
Sophomore	F	No	3.0	3	73	120	1	1	3.95	89
FirstYear	M	No	24.0	6	78	225	2	1	2.10	78
FirstYear	F	No	3.0	1	65	160	1	2	3.00	83
Sophomore	F	No	6.0	1	63	120	2	1	3.00	58
Sophomore	F	No	12.0	10	68	138	1	2	3.75	77
Sophomore	M	No	18.0	3	72	260	2	3	2.50	50
Sophomore	M	No	2.0	7	70	150	2	3	3.40	87
FirstYear	F	No	12.0	3	67	135	3	4	3.40	74
Sophomore	F	No	5.0	10	72	165	1	1	3.14	76
FirstYear	M	No	3.0	3	68	142	3	4	2.60	50
Sophomore	M	No	3.0	3	78	210	6	5	3.40	70
Sophomore	M	No	21.0	25	69	171	1	1	2.70	84
Sophomore	F	No	12.0	2	80	150	4	1	3.15	68
Sophomore	M	No	3.0	15	71	188	3	1	2.20	66
Sophomore	M	No	20.0	6	70	195	0	1	3.50	76
FirstYear	M	No	8.0	13	75	230	2	1	2.90	65
Sophomore	F	No	2.0	3	64	140	2	3	2.50	65
Sophomore	M	No	15.0	2	78	200	1	1	3.50	68
Senior	F	No	6.0	5	68	140	0	1	3.60	78
FirstYear	F	No	2.0	1	69	180	5	3	3.10	74
Sophomore	F	No	1.0	4	63	160	1	1	3.00	76
Sophomore	F	No	13.0	5	64	135	3	2	3.00	79
Sophomore	F	No	12.0	10	63	140	2	3	3.80	81
Sophomore	F	No	10.0	4	72	155	2	1	3.15	56
Sophomore	M	No	10.0	3	63	235	5	3	2.75	48
FirstYear	F	No	10.0	2	63	140	3	2	2.80	68
Sophomore	F	No	3.0	4	68	130	2	3	3.00	62
Junior	F	No	2.0	3	67	125	5	4	3.10	70
FirstYear	M	No	10.0	3	71	222	1	1	2.27	46
FirstYear	F	No	4.0	3	65	128	3	1	2.80	88
FirstYear	M	No	8.0	2	72	183	2	2	3.02	68
Junior	M	No	18.0	20	75	175	0	1	2.93	74
FirstYear	F	No	5.0	3	59	125	1	1	3.20	88
Sophomore	F	No	4.0	4	69	156	1	1	3.00	67
FirstYear	F	No	20.0	3	63	145	3	4	3.00	61
Sophomore	M	No	14.0	4	74	195	4	2	2.70	62
Sophomore	M	No	8.0	13	70	185	2	1	3.20	69
FirstYear	F	No	4.0	5	64	150	1	1	2.90	59
Sophomore	F	No	5.0	5	67	140	0	NA	3.00	79
FirstYear	M	No	14.0	4	66	150	1	1	2.72	56
FirstYear	F	No	4.0	3	67	150	0	1	3.30	85
Sophomore	M	No	4.0	10	73	220	1	2	NA	72
Senior	M	No	15.0	10	71	195	2	3	2.22	69
Sophomore	F	No	12.0	7	66	140	1	2	3.26	61
FirstYear	F	No	10.0	10	68	135	2	3	3.50	95
Sophomore	F	No	6.0	3	67	138	1	1	3.10	58
Senior	F	No	12.0	5	69	170	2	3	3.30	57
Sophomore	F	No	10.0	2	66	145	1	1	3.29	80
FirstYear	M	No	14.0	5	68	135	2	3	NA	60
FirstYear	F	No	5.0	4	68	140	0	1	3.69	69
Sophomore	M	No	18.0	5	71	155	2	2	2.65	73
Senior	M	No	10.0	10	70	155	1	2	3.25	62
Sophomore	M	No	8.0	2	66	155	1	1	2.80	64
Sophomore	F	No	8.0	10	65	135	2	3	3.36	86
Junior	M	No	3.0	15	70	165	1	1	2.97	73
FirstYear	M	No	5.0	20	71	160	2	1	3.31	71
Sophomore	M	No	4.0	21	71	175	1	1	3.05	72
Sophomore	M	No	8.0	10	70	183	3	2	2.20	84
Sophomore	F	No	3.0	10	65	140	2	3	3.30	120
Sophomore	F	No	12.0	4	67	140	1	1	3.45	77
Junior	F	No	5.0	10	61	110	2	2	3.83	80
Sophomore	F	No	5.0	3	68	125	0	1	3.00	80
Senior	F	No	15.0	2	65	125	2	2	3.35	54
FirstYear	M	No	10.0	7	70	180	2	3	2.40	54
Sophomore	M	No	10.0	10	72	195	2	3	3.10	78
Sophomore	F	No	10.0	6	66	128	3	3	3.40	72
FirstYear	M	No	14.0	2	71	172	1	1	2.82	78
Sophomore	F	No	6.0	4	64	150	1	1	2.90	69
Sophomore	M	No	4.0	27	73	188	1	1	3.40	80
Sophomore	F	No	14.0	2	60	110	2	1	3.20	76
Sophomore	F	No	5.0	15	64	125	1	1	3.20	74
Sophomore	F	No	16.0	10	65	135	3	1	3.80	70
FirstYear	F	No	14.0	3	65	130	2	2	3.57	72
Sophomore	M	No	10.0	10	73	230	2	2	3.33	60
Sophomore	M	No	11.0	10	69	198	1	2	2.90	71
Sophomore	F	No	4.0	10	66	127	1	2	3.20	70
Sophomore	M	No	12.0	5	66	150	1	2	3.10	53
Sophomore	M	No	5.0	4	73	175	3	1	3.25	70
Junior	M	No	8.0	14	71	160	3	4	3.40	75
Junior	F	No	8.0	6	65	140	2	3	3.80	84
Sophomore	M	No	3.0	5	75	200	1	1	3.38	66
Sophomore	F	No	8.0	2	63	130	1	1	3.88	72
Sophomore	M	No	20.0	14	74	210	3	3	2.75	70
Sophomore	M	No	10.0	5	70	210	2	2	2.90	49
Sophomore	F	No	3.0	3	63	145	4	5	3.60	81
Sophomore	M	No	4.0	6	75	156	3	1	2.80	77
FirstYear	M	No	8.0	10	71	207	0	1	2.20	72
FirstYear	F	No	15.0	5	68	150	1	2	NA	38
Sophomore	F	No	14.0	10	68	137	2	2	3.30	60
FirstYear	M	No	14.0	2	72	153	2	3	2.85	64
Junior	F	No	12.0	5	63	175	2	3	3.37	65
Sophomore	F	No	6.0	2	65	136	3	1	3.50	72
Sophomore	F	No	3.0	10	65	104	2	2	3.55	54
FirstYear	F	No	12.0	3	67	122	3	4	3.20	82
Sophomore	M	No	5.0	40	72	192	1	1	2.47	82
FirstYear	M	No	8.0	10	71	218	1	2	2.72	62
Sophomore	M	No	1.0	14	68	170	4	5	3.40	52
FirstYear	M	No	10.0	4	72	220	2	2	NA	66
Sophomore	F	No	7.0	2	64	150	1	1	3.40	55
Senior	M	No	5.0	7	71	135	4	3	3.10	63
Senior	F	No	10.0	2	62	155	1	1	3.10	78
Sophomore	F	No	12.0	5	65	135	1	1	2.94	65
Sophomore	M	No	15.0	15	68	140	1	2	3.00	64
FirstYear	F	No	10.0	5	67	120	1	1	NA	70
Sophomore	F	No	7.0	12	68	135	3	1	3.60	70
Sophomore	F	No	NA	4	64	135	1	1	3.60	65
Sophomore	M	No	15.0	0	72	165	2	1	3.50	71
Junior	M	No	10.0	15	71	180	1	2	3.40	54
Sophomore	M	No	15.0	0	72	165	2	1	3.50	71
Sophomore	M	No	12.0	6	72	175	2	2	3.00	54
Sophomore	M	No	10.0	5	71	200	1	2	2.75	70
Sophomore	M	No	12.0	10	71	138	0	1	3.56	65
Senior	M	No	5.0	3	71	265	1	1	2.70	82
Sophomore	F	No	14.0	16	61	105	1	2	3.68	63
Sophomore	F	No	3.0	9	68	130	3	3	3.50	71
Sophomore	M	No	12.0	2	70	165	1	1	3.50	75
Sophomore	F	No	15.0	5	67	145	1	2	3.40	60
FirstYear	F	No	3.0	6	64	138	1	1	2.60	54
Sophomore	F	No	25.0	12	71	193	2	2	3.25	68
Sophomore	M	No	5.0	1	71	170	1	1	3.30	70
Sophomore	M	No	6.0	0	69	155	1	1	3.20	90
Sophomore	M	No	27.0	2	70	155	1	1	2.90	72
Junior	F	No	8.0	10	65	140	2	1	3.85	41
Sophomore	F	No	3.0	1	65	130	1	1	3.40	80
Sophomore	M	No	17.0	14	72	180	3	3	3.40	68
FirstYear	M	No	40.0	2	67	140	2	2	NA	64
Sophomore	M	No	5.0	10	74	210	1	2	2.70	78
Sophomore	M	No	0.0	7	NA	150	0	1	3.81	65
Sophomore	F	No	27.0	2	62	115	1	2	3.40	64
Sophomore	M	No	3.0	5	75	225	3	1	3.23	78
FirstYear	M	No	3.0	7	67	170	2	3	3.10	42
Sophomore	F	No	11.0	20	63	120	0	1	2.89	60
Senior	M	No	2.0	4	71	170	1	1	2.81	59
Sophomore	F	No	9.0	1	63	130	2	3	3.00	54
FirstYear	M	No	12.0	8	70	182	1	2	3.77	70
Sophomore	M	No	15.0	2	67	138	1	2	3.30	52
Sophomore	M	No	2.0	5	74	180	2	1	3.00	88
Sophomore	M	No	20.0	6	69	230	0	1	2.90	60
Junior	M	No	12.0	5	70	222	2	1	3.50	66
FirstYear	M	No	5.0	2	70	145	4	4	3.60	55
Sophomore	M	No	10.0	4	70	150	1	1	3.70	74
Senior	M	No	2.0	2	68	190	0	1	3.20	59
Sophomore	M	No	12.0	20	76	195	3	1	2.87	84
Sophomore	F	No	5.0	2	59	115	1	2	3.30	68
Junior	F	No	3.0	1	66	140	1	2	3.30	74
Sophomore	M	No	12.0	10	68	155	1	1	3.45	58
Sophomore	M	No	8.0	3	72	150	2	1	3.10	62
Sophomore	M	No	8.0	4	69	155	2	1	3.71	84
Sophomore	M	No	5.0	3	NA	130	2	1	3.30	72
FirstYear	M	No	6.0	14	75	210	3	2	3.30	52
	F	No	8.0	10	63	105	3	1	NA	80
Junior	M	No	10.0	10	71	192	1	1	3.73	68
FirstYear	F	No	18.0	3	72	220	3	4	3.13	71
Junior	F	No	12.0	0	64	134	1	2	3.89	55
Sophomore	M	No	10.0	5	68	160	1	1	3.05	68
Junior	M	No	10.0	5	68	135	1	1	3.20	61
Sophomore	M	No	5.0	2	67	140	1	1	3.25	80
Sophomore	F	No	7.0	2	66	135	0	1	2.90	66
FirstYear	M	No	3.0	5	74	145	1	2	3.00	70
FirstYear	F	No	7.0	4	64	140	2	1	3.50	78
Sophomore	F	No	3.0	2	NA	NA	2	2	3.50	88
Sophomore	F	No	4.0	3	65	138	2	2	3.60	72
FirstYear	F	No	8.0	4	64	NA	2	2	3.40	65
Sophomore	F	No	7.0	5	64	130	2	2	3.25	63
Senior	M	No	7.0	9	72	210	2	2	2.70	70
Senior	M	No	3.0	1	69	233	1	1	3.78	72
FirstYear	F	No	7.0	7	70	180	6	7	4.00	63
FirstYear	M	No	14.0	6	67	185	1	1	3.00	68
Sophomore	M	No	5.0	6	76	189	3	2	3.30	64
FirstYear	F	No	14.0	5	66	127	1	1	2.80	64
Senior	M	No	5.0	4	63	135	1	1	2.50	60
Sophomore	F	No	5.0	5	66	140	0	1	3.50	68
Sophomore	F	No	2.0	20	68	162	2	1	2.80	70
Sophomore	F	No	1.0	3	67	215	0	1	3.40	63
Senior	M	No	15.0	5	73	200	2	1	3.00	57
Sophomore	F	No	5.0	1	62	120	1	1	3.27	84
FirstYear	M	No	5.0	2	67	165	3	4	3.50	74
FirstYear	M	No	15.0	14	71	175	2	3	3.00	61
Sophomore	F	No	5.0	3	66	160	2	1	3.60	78
Sophomore	M	No	20.0	0	68	145	1	2	3.25	65
Junior	F	No	3.0	5	60	180	3	4	3.00	68
FirstYear	F	No	7.0	0	71	170	1	1	2.75	76
Sophomore	M	No	20.0	10	75	235	2	1	2.90	54
Sophomore	F	No	10.0	10	65	155	1	1	3.00	56
Senior	M	No	6.0	15	65	140	3	3	3.00	88
Sophomore	F	No	6.0	1	66	145	2	2	2.90	77
FirstYear	M	No	10.0	3	71	175	2	2	3.36	52
Sophomore	M	No	9.0	6	76	210	2	2	3.25	62
FirstYear	F	No	1.5	20	67	130	1	1	3.50	80
Sophomore	M	No	20.0	28	72	195	1	1	2.76	60
Sophomore	M	No	8.0	3	67	165	1	2	NA	67
Sophomore	M	No	21.0	1	73	180	6	3	2.75	51
Sophomore	F	No	10.0	5	60	145	1	2	3.25	81
Sophomore	M	No	8.0	12	70	163	2	1	3.00	62
Junior	M	No	10.0	1	75	160	1	2	2.80	84
Junior	F	No	18.0	7	67	150	1	1	3.40	75
Sophomore	M	No	15.0	6	71	170	3	1	3.25	60
Sophomore	F	No	8.0	5	NA	110	3	3	3.50	76
Senior	M	No	6.0	2	66	170	1	2	3.05	65
Sophomore	M	No	12.0	3	69	145	2	2	3.18	65
FirstYear	F	No	10.0	4	69	160	1	2	3.00	64
Junior	F	No	7.0	4	63	130	1	1	2.23	75
Sophomore	F	No	5.0	5	65	155	1	1	3.40	93
FirstYear	F	No	6.0	4	65	NA	1	2	3.30	75
Senior	M	No	5.0	5	72	160	2	3	3.43	82
Sophomore	F	No	5.0	5	66	151	1	1	3.88	80
Sophomore	M	No	30.0	10	74	180	1	1	3.45	69
Senior	F	No	5.0	4	64	130	2	3	3.00	85
Junior	M	Yes	12.0	5	75	185	1	2	3.00	76
Senior	M	Yes	0.0	1	73	198	1	1	3.18	76
FirstYear	M	Yes	12.0	5	72	175	2	3	2.20	65
Senior	F	Yes	0.0	14	67	123	1	1	3.29	67
Junior	F	Yes	15.0	10	64	145	1	1	3.50	64
FirstYear	M	Yes	18.0	15	67	190	0	1	2.80	71
Sophomore	F	Yes	12.0	5	65	130	2	3	2.90	65
Sophomore	M	Yes	2.0	3	70	185	4	3	3.50	83
FirstYear	M	Yes	12.0	20	68	165	1	1	2.50	65
Sophomore	M	Yes	3.0	5	70	165	3	2	3.25	77
Junior	M	Yes	3.0	3	67	150	2	2	2.90	66
FirstYear	M	Yes	4.0	3	72	160	1	2	3.66	62
Junior	F	Yes	12.0	2	64	142	3	3	3.01	58
FirstYear	M	Yes	25.0	5	72	165	1	1	2.25	48
Junior	M	Yes	3.0	4	75	175	0	1	3.20	61
Sophomore	M	Yes	6.0	6	69	175	2	1	3.35	50
Sophomore	F	Yes	7.0	8	68	190	1	1	3.00	72
Sophomore	M	Yes	7.0	2	72	180	2	2	3.00	74
Sophomore	M	Yes	6.0	2	74	185	1	2	3.48	80
Sophomore	M	Yes	6.0	2	NA	NA	1	1	2.88	90
Sophomore	F	Yes	13.0	4	64	135	3	2	2.60	72
Sophomore	M	Yes	25.0	8	73	195	1	1	2.75	64
Senior	M	Yes	8.0	12	71	175	0	1	3.30	72
Sophomore	M	Yes	5.0	5	70	165	1	1	3.25	70
FirstYear	M	Yes	11.0	6	68	135	1	1	3.30	84
Sophomore	F	Yes	18.0	5	69	140	1	1	3.20	87
Sophomore	M	Yes	10.0	NA	NA	182	2	1	2.60	60
FirstYear	M	Yes	6.0	14	72	155	1	2	3.00	60
FirstYear	F	Yes	2.0	1	68	180	2	3	3.25	80
Senior	M	Yes	5.0	25	69	170	1	1	3.30	70
Sophomore	F	Yes	5.0	3	66	135	3	2	3.25	78
FirstYear	M	Yes	6.0	25	72	165	2	1	2.83	75
Sophomore	F	Yes	10.0	10	65	137	0	1	3.30	42
Sophomore	M	Yes	4.0	1	70	147	2	2	3.60	80
Senior	F	Yes	5.0	4	66	150	1	2	3.70	72
Junior	F	Yes	17.0	2	67	155	2	1	2.83	96
Sophomore	M	Yes	7.0	10	71	160	2	3	3.30	95
Sophomore	F	Yes	2.0	0	83	130	1	1	3.44	80
Sophomore	M	Yes	8.0	10	61	180	2	1	3.00	74
Sophomore	F	Yes	1.0	1	65	150	2	2	3.27	78
FirstYear	M	Yes	14.0	5	77	205	2	2	2.30	72
Sophomore	F	Yes	12.0	5	60	115	0	1	2.60	91

Distribution

In the given dataset, there are multiple variables (such as Gender, Smoke, Exercise, Height, Weight, etc.) for different students across various academic years.

Knowing the distribution of each variable can help us identify relationships, trends, and potential anomalies in the data.

Distribution

“The distribution of the variable Y” describes its center, variability, and shape using both numbers and graphics.

Center: Mean or Average

Mean: Average value in a sample or population.
- Sample mean: \(\bar{y} = \dfrac{\sum_{i=1}^n y_i}{n}\)
- Population mean: \(\mu\)

mean(survey$Pulse)

[1] 69.57459

The mean pulse rate for this sample of students is \(\bar{y} = 69.6\) beats per minute.

Center: Median

Median: The middle value when the data are ordered.
- Sample median: \(m\)
- Population median: \(M\)

median(survey$Pulse)

[1] 70

The median pulse rate for this sample of students is \(m = 70\) beats per minute.

Variability: Standard Deviation

Standard Deviation (SD): Average deviation from the center in a sample or population.
- Sample SD: \(s = \sqrt{ \dfrac{\sum_{i=1}^n (y_i - \overline{y})^2}{n-1}}\)
- Population SD: \(\sigma\)

sd(survey$Pulse)

[1] 12.20514

The SD of pulse rates for this sample of students is \(s = 12.2\) beats per minute. The “average” deviation of individual pulse rates around the mean value is about 12.2 beats per minute.

Day 3

Descriptive Statistics

One Qualitative Variable

Frequency Table

Proportion

What proportion of adults sampled do not own a cell phone?

Bar Chart

Two Qualitative Variables

Relationship Status and Gender

Difference in Proportions

Student Survey

Distribution

Distribution

Center: Mean or Average

Center: Median

Variability: Standard Deviation