Charlene M.

Quirino
Masters of arts in Nursing
Problem # 1
1. Frequency Distribution Table
Class Count Relative Frequency
58 - 65 2 8
66 - 73 4 16
74 - 81 6 24
82 - 89 8 32
90 - 97 5 20
Total 25 100
2. Mean :
µ=
58+63+66+70+72+73+74+77+78+79+80+81+82+84+85+85+87+88+88+89+91+92+93+94+95 /25
µ= 2024/25
µ= 80.96
3. Median = 82
4. Mode = 85,88
5. Interquartile Range (IQR):
Calculate the first quartile (Q1) and the third quartile (Q3).
58 63 66 70 72 73 74 77 78 79 80 81 82 84 85 85 87 88 88 89 91 92 93 94 95
Q 1 = 73 .5
58 63 66 70 72 73 74 77 78 79 80 81 82 84 85 85 87 88 88 89 91 92 93 94 95
Q3= 88 .5
Compute the interquartile range (IQR).
IQR = 88.5– 73.5 =15
6.Standard Deviation

X Xi-µ (Xi-µ)2
58 -22.96 527.16
63 -17.96 322.56
66 -14.96 223.80
70 -10.96 120.12
72 -8.96 80.28
73 -7.96 63.36
74 -6.96 48.44
77 -3.96 15.68
78 -2.96 8.76
79 -1.96 3.84
80 -0.96 0.92
81 0.04 0.00
82 1.04 1.08
84 3.04 9.24
85 4.04 16.32
85 4.04 16.32
87 6.04 36.48
88 7.04 49.56
88 7.04 49.56
89 8.04 64.64
91 10.04 100.80
92 11.04 121.88
93 12.04 144.96
94 13.04 170.04
95 14.04 197.12
∑(Xi-µ)2 = 2392.96

σ= √2392.96/24
σ= √99.71
σ= 9.99
Problem #2
1. Frequency Distribution Table
Class Count Relative Frequency
110-117 2 10
118 - 125 7 35
126 - 133 4 20
134 - 141 5 25
142 - 149 2 10
Total 20 100
2. Mean:
µ=110+115+118+119+120+122+125+125+125+126+128+130+132+134+135+136+138+140+1
42+145
µ= 2565/ 20
µ= 128.25
3. Median = 127
4. Mode = 125
5.InterquartileRange(IQR):
Calculate the first quartile(Q1) and the third quartile(Q3).
110 115 118 119 120 122 125 125 125 126 128 130 132 134 135 136 138 140 142 145
Q 1 =121
110 115 118 119 120 122 125 125 125 126 128 130 132 134 135 136 138 140 142 145
Q3=135.5
Compute the interquartile range (IQR).
IQR = 135.5–121=14
6.Standard Deviation

X Xi-µ (Xi-µ)2
110 -18.85 333.06
115 -13.35 175.56
118 -10.25 105.06
119 -9.25 85.56
120 -8.25 68.06
122 -6.25 39.06
125 -3.25 10.56
125 -3.25 10.56
125 -3.25 10.56
126 -2.25 5.06
128 -0.25 0.06
130 1.75 3.06
132 3.75 14.06
134 5.75 33.06
135 6.75 45.56
136 7.75 60.06
138 9.75 95.06
140 11.75 138.06
142 13.75 189.06
145 16.75 280.56
∑(Xi-µ)2 = 1701.75
σ= √1701.75/19
σ= √89.57
σ= 9.46
Problem 3
1. Frequency Distribution Table
Class Count Relative Frequency
50-57 2 13.3
58 -65 5 33. 3
66 - 73 5 33.3
74 - 81 2 13.3
84 - 89 1 6.7
Total 15 100
2.Mean: µ=54+55+58+59+61+64+65+67+68+71+72+73+76+77+85 15
µ= 1005 /15
µ= 67
3.Median = 67
4.Mode = All values appeared once
5.InterquartileRange(IQR):
Calculate the first quartile(Q1) and the third quartile (Q3).
54 55 58 59 61 64 65 67 68 71 72 73 76 77 85
Q 1 =59
54 55 58 59 61 64 65 67 68 71 72 73 76 77 85
Q3=73
Compute the interquartile range (IQR).
IQR = 73–59=14
6.Standard Deviation

X Xi-µ (Xi-µ)2
54 -13 169
55 -12 144
58 -9 81
59 -8 64
61 -6 36
64 -3 9
65 -2 4
67 0 0
68 1 1
71 4 16
72 5 25
73 6 36
76 9 81
77 10 100
85 18 324
∑(Xi-µ)2 = 1090
σ= √1090/14
σ= √77.86
σ= 8.82
7.Skewness
Skewness: 0.27
There is a weak positive skewness-indicating that the data is approximately symmetric,
with a slight skew to the right.
8. Kurtosis
Kurtosis: -0.66
The distribution is platykurtic. It has a has low negative kurtosis, indicating that it is
relatively flat and fewer outliers than a normal distribution.

Problem 4
1. Frequency Distribution Table
Class Count Relative Frequency
10-13.4 5 25
13.5 -16.9 5 25
17 – 20.4 5 25
20.5 – 23.9 3 10
24 – 27.4 2 10
Total 20 100

2. Mean: µ=10+12+15+20+18+25+22+14+19+17+13+16+11+15+21+18+14+23+12+24
µ= 339/20
µ= 16.95
3.Mode = 12,15,18,14
4. Inter quartile Range (IQR):
Calculate the first quartile (Q1) and the third quartile (Q3).
10 11 12 12 13 14 14 15 15 16 17 18 18 19 20 21 22 23 24 25
Q 1 =13 .5
10 11 12 12 13 14 14 15 15 16 17 18 18 19 20 21 22 23 24 25
Q3=20 .5
Compute the interquartile range (IQR).
IQR = 20.5– 13.5 =7
6.Standard Deviation

X Xi-µ (Xi-µ)2
10 -6.95 48.30
12 -4.95 24.50
15 -1.95 3.80
20 3.05 9.30
18 1.05 1.10
25 8.05 64.80
22 5.05 25.50
14 -2.95 8.70
19 2.05 4.20
17 0.05 0.00
13 -3.95 15.60
16 -0.95 0.90
11 -5.95 35.40
15 -1.95 3.80
21 4.05 16.40
18 1.05 1.10
14 -2.95 8.70
23 6.05 36.60
12 -4.95 24.50
24 7.05 49.70
∑(Xi-µ)2 = 382.95

σ= √382.95/19
σ= √20.16
σ= 4.49
7.Skewness
Skewness: 0.24 There is a weakpositiveskewness-indicating that the data is
approximately symmetric, with a slight skew to the right.
8. Kurtosis: -1.06
 The distribution is platykurtic. It has a relatively low number of outliers.

Problem 5
1. Frequency Distribution Table
Class Count Relative Frequency
2800-3249 6 20
3250 -3699 7 23.3
3700 –4149 7 23.3
4150 –4599 4 13. 3
4600 – 5049 5 16.7
5050-5499 1 3.3
Total 30 100
2. Mean:
µ=3200+4500+3500+2800+5000+3400+3700+3300+4100+4600+4800+3000+3200+3900+3400+
5200+4300+2900+3500+3400+4000+3700+4500+4100+4400+4800+3900+ 3600+3000+4900
µ= 116600/ 30
µ= 3886.67
3.Median = 3800
4.Mode = 3400
5.InterquartileRange(IQR):
Calculate the first quartile (Q1) and the third quartile (Q3).
2800 2900 3000 3000 3200 3200 3300 3400 3400 3400 3500 3500 3600 3700 3700 3900 3900
4000 4100 4100 4300 4400 4500 4500 46 00 4800 4800 4900 5000 5200
Q1=3400
2800 2900 3000 3000 3200 3200 3300 3400 3400 3400 3500 3500 3 600 3700 3700 3900 3900
4000 4100 4100 4300 4400 4500 4500 46 00 4800 4800 4900 5000 5200
Q3=4500
Compute the interquartile range (IQR).
IQR=4500-3400=1100

6.Standard Deviation

X Xi-µ (Xi-µ)2
3200 -686.67 471511.17
4500 613.33 376177.74
3500 -386.67 149511.14
2800 -1086.67 1180844.52
5000 1113.33 1239511.04
3400 -486.67 236844.48
3700 -186.67 34844.46
3300 -586.67 344177.82
4100 213.33 45511.10
4600 713.33 508844.40
4800 913.33 834177.72
3000 -886.67 786177.84
3200 -686.67 471511.17
3900 13.33 177.78
3400 -486.67 236844.48
5200 1313.33 1724844.36
4300 413.33 170844.42
2900 -986.67 973511.18
3500 -386.67 149511.14
3400 -486.67 236844.48
4000 113.33 12844.44
3700 -186.67 34844.46
4500 613.33 376177.74
4100 213.33 45511.10
4400 513.33 263511.08
4800 913.33 834177.72
3900 13.33 177.78
3600 -286.67 82177.80
3000 -886.67 786177.84
4900 1013.33 1026844.38
∑(Xi-µ)2 = 13634666.67

σ= √13634666.67/29
σ= √470160.92
σ= 685.68
7.Skewness
Skewness: 0.25

There is a weak positive Skewness indicating that the data is approximately symmetric,
with a slight skew to the right.
8.Kurtosis: -1.07
The distribution is platykurtic. It has a relatively low number of outliers.