Question

1. The data are from the U.S. Department of Health and Human Services, National Center of Health Statistics, Third National Health and Nutrition Examination Survey. The systolic blood pressure (mmHg) for 80 patients was measured. The following data is separated by gender Females: 89 92 93 93 94 95 97 98 99 100 101 102 104 104 104 105 106 106 107 107 107 108 108 110 112 113 113 114 114 116 116 118 119 123 124 125 127 133 155 181 95 107 107 109 109 110 110 110 110 110 112 112 112 112 113 Males: 113 115 115 116 116 118 119 120 121 121 124 125 125 125 125 125 126 126 127 131 131 132 132 137 153 2. Use the same data and combine the two sets of data into one Calculate the values that are two standard deviations from the mean. Are there any values that are more than two standard deviations from the mean? List them Construct a boxplot. Identify any outliers e. f.

Answer 1

1.

I have used excel for sorting the data.

1. Input the data one after the other for the genders.
2. Using the sorting tool for pressure, we will sort the pressure values.

Gender	Pressure
Female	89
Female	92
Female	93
Female	93
Female	94
Female	95
Male	95
Female	97
Female	98
Female	99
Female	100
Female	101
Female	102
Female	104
Female	104
Female	104
Female	105
Female	106
Female	106
Female	107
Female	107
Female	107
Male	107
Male	107
Female	108
Female	108
Male	109
Male	109
Female	110
Male	110
Male	110
Male	110
Male	110
Male	110
Female	112
Male	112
Male	112
Male	112
Male	112
Female	113
Female	113
Male	113
Male	113
Female	114
Female	114
Male	115
Male	115
Female	116
Female	116
Male	116
Male	116
Female	118
Male	118
Female	119
Male	119
Male	120
Male	121
Male	121
Female	123
Female	124
Male	124
Female	125
Male	125
Male	125
Male	125
Male	125
Male	125
Male	126
Male	126
Female	127
Male	127
Male	131
Male	131
Male	132
Male	132
Female	133
Male	137
Male	153
Female	155
Female	181

e.

Gender	Pressure (x)	$x_{i}-\bar{x}$	$(x_{i}-\bar{x})^{2}$
Female	89	-25.85	668.22
Female	92	-22.85	522.12
Female	93	-21.85	477.42
Female	93	-21.85	477.42
Female	94	-20.85	434.72
Female	95	-19.85	394.02
Male	95	-19.85	394.02
Female	97	-17.85	318.62
Female	98	-16.85	283.92
Female	99	-15.85	251.22
Female	100	-14.85	220.52
Female	101	-13.85	191.82
Female	102	-12.85	165.12
Female	104	-10.85	117.72
Female	104	-10.85	117.72
Female	104	-10.85	117.72
Female	105	-9.85	97.02
Female	106	-8.85	78.32
Female	106	-8.85	78.32
Female	107	-7.85	61.62
Female	107	-7.85	61.62
Female	107	-7.85	61.62
Male	107	-7.85	61.62
Male	107	-7.85	61.62
Female	108	-6.85	46.92
Female	108	-6.85	46.92
Male	109	-5.85	34.22
Male	109	-5.85	34.22
Female	110	-4.85	23.52
Male	110	-4.85	23.52
Male	110	-4.85	23.52
Male	110	-4.85	23.52
Male	110	-4.85	23.52
Male	110	-4.85	23.52
Female	112	-2.85	8.12
Male	112	-2.85	8.12
Male	112	-2.85	8.12
Male	112	-2.85	8.12
Male	112	-2.85	8.12
Female	113	-1.85	3.42
Female	113	-1.85	3.42
Male	113	-1.85	3.42
Male	113	-1.85	3.42
Female	114	-0.85	0.72
Female	114	-0.85	0.72
Male	115	0.15	0.02
Male	115	0.15	0.02
Female	116	1.15	1.32
Female	116	1.15	1.32
Male	116	1.15	1.32
Male	116	1.15	1.32
Female	118	3.15	9.92
Male	118	3.15	9.92
Female	119	4.15	17.22
Male	119	4.15	17.22
Male	120	5.15	26.52
Male	121	6.15	37.82
Male	121	6.15	37.82
Female	123	8.15	66.42
Female	124	9.15	83.72
Male	124	9.15	83.72
Female	125	10.15	103.02
Male	125	10.15	103.02
Male	125	10.15	103.02
Male	125	10.15	103.02
Male	125	10.15	103.02
Male	125	10.15	103.02
Male	126	11.15	124.32
Male	126	11.15	124.32
Female	127	12.15	147.62
Male	127	12.15	147.62
Male	131	16.15	260.82
Male	131	16.15	260.82
Male	132	17.15	294.12
Male	132	17.15	294.12
Female	133	18.15	329.42
Male	137	22.15	490.62
Male	153	38.15	1455.42
Female	155	40.15	1612.02
Female	181	66.15	4375.82
Total	9188	0.00	17004.2

Mean = $\frac{\sum x }{n}$ = $\frac{9188}{80}$

Mean = $\mathbf{114.85}$

Std dev = $\sqrt{Var}$

=  $\sqrt{\frac{\sum (x_{i}-\bar{x})^{2}}{n-1}}$

= $\sqrt{\frac{17004.2}{80-1}}$

= $\mathbf{14.67}$

$\mu-2\sigma$ = 114.85 - 2*14.67 = 85.508

$\mu+2\sigma$ = 114.85 + 2*14.67 = 144.19

The values that are outside the range are

Male	153
Female	155
Female	181

f.

For boxplot we need five values those are

Values	X
Min	89
Lower quartile (Q1) [20.25th value]	107
Median (Q2) [40.5th value]	113
Upper quartile (Q3) [60.75th value]	124
Max	181

To find the quartile value we have

$Q_{i}=({\frac{i(N+1)}{4}})^{th}value$

Boxplot

107 113 124 181 80 90 100 110 120 130 150 160 170 180 190 200 140 Pressure

For checking the outliers we need to see if any value is $Q_{1}-1.5IQR<x<Q_{3}&plus;1.5IQR$

Where $IQR=Q_{1}-Q_{3}$

= 17

$Q_{1}-1.5IQR$ = 107 - 1.5*17 = 81.5

$Q_{3}&plus;1.5IQR$ = 124 - 1.5 * 17 = 149.5

The values that fall outside this range are

Male	153
Female	155
Female	181