Descriptive Statistics Sample Assignment
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Class Interval Frequency
10-under 15 6
15-under 20 22
20-under 25 35
25-under 30 29
30-under 35 16
35-under 40 8
40-under 45 4
45-under 50 2
Answer:-
The mean is computed as follows.
Class ____ f __ M _ fM
10-under 15 6______12.5 75.0
15-under 20 22_____17.5 385.0
20-under 25 35_____22.5 787.5
25-under 30 29_____27.5 797.5
30-under 35 16_____32.5 520.0
35-under 40 8______37.5 300.0
40-under 45 4______42.5 170.0
45-under 50 2______47.5 95.0
_____ ∑f = n = 122_______∑fM = 3130.0
x = ∑fM = 3130 = 25.66
∑f 122
The grouped mean is 25.66.
The grouped mode can be determined by finding the class midpoint of the class interval with the greatest frequency. The class with the greatest frequency is 20-under 25 with a frequency of 35. The midpoint of this class is 22.5, which is the grouped mode.
The variance and standard deviation can be found as shown next. First, use the original formula.
Class____ f __ M _ M – x (M – x)2 ___ f(M – x)2
10-under 15 6___12.5 75.0_____173.19_____1039.14
15-under 20 22 17.5 385.0____66.59______1464.98
20-under 25 35 22.5 787.5____9.99_______349.65
25-under 30 29 27.5 797.5____3.39_______98.31
30-under 35 16 32.5 520.0____46.79______748.64
35-under 40 8__37.5____300.0____140.19_____1121.52
40-under 45 4 42.5____170.0____283.59_____1134.36
45-under 50 2 47.5____95.0_____476.99_____953.98
_____∑f = n = 122__________________∑f(M – x)2 = 6910.58
S2 = ∑f(M – x)2 = 6910.58 = 57.11
_____n – 1__ 121
S = √57.11 = 7.56
Next, use the computational formula.
Class ____ f __ M _ fM _____ fM2
10-under 15 6____12.5__75.0________937.50
15-under 20 22___17.5__385.0_______6,737.50
20-under 25 35___22.5__787.5_______17,718.75
25-under 30 29___27.5__797.5_______21,931.25
30-under 35 16___32.5__520.0_______16,900.00
35-under 40 8____37.5__300.0_______11,250.00
40-under 45 4____42.5__170.0_______7,225.00
45-under 50 2____47.5__95.0________4,512.50
∑f = n = 122 ∑fM = 3,130.0 ∑fM2 = 87,212.50
S = √57.11 = 7.56
The sample variance is 57.11 and the standard deviation is 7.56.
Descriptive Statistics Sample Assignment
Compute the mean, mode, variance, and standard deviation on the following sample data.
Questions: -Class Interval Frequency
10-under 15 6
15-under 20 22
20-under 25 35
25-under 30 29
30-under 35 16
35-under 40 8
40-under 45 4
45-under 50 2
Answer:-
The mean is computed as follows.
Class ____ f __ M _ fM
10-under 15 6______12.5 75.0
15-under 20 22_____17.5 385.0
20-under 25 35_____22.5 787.5
25-under 30 29_____27.5 797.5
30-under 35 16_____32.5 520.0
35-under 40 8______37.5 300.0
40-under 45 4______42.5 170.0
45-under 50 2______47.5 95.0
_____ ∑f = n = 122_______∑fM = 3130.0
x = ∑fM = 3130 = 25.66
∑f 122
The grouped mean is 25.66.
The grouped mode can be determined by finding the class midpoint of the class interval with the greatest frequency. The class with the greatest frequency is 20-under 25 with a frequency of 35. The midpoint of this class is 22.5, which is the grouped mode.
The variance and standard deviation can be found as shown next. First, use the original formula.
Class____ f __ M _ M – x (M – x)2 ___ f(M – x)2
10-under 15 6___12.5 75.0_____173.19_____1039.14
15-under 20 22 17.5 385.0____66.59______1464.98
20-under 25 35 22.5 787.5____9.99_______349.65
25-under 30 29 27.5 797.5____3.39_______98.31
30-under 35 16 32.5 520.0____46.79______748.64
35-under 40 8__37.5____300.0____140.19_____1121.52
40-under 45 4 42.5____170.0____283.59_____1134.36
45-under 50 2 47.5____95.0_____476.99_____953.98
_____∑f = n = 122__________________∑f(M – x)2 = 6910.58
S2 = ∑f(M – x)2 = 6910.58 = 57.11
_____n – 1__ 121
S = √57.11 = 7.56
Next, use the computational formula.
Class ____ f __ M _ fM _____ fM2
10-under 15 6____12.5__75.0________937.50
15-under 20 22___17.5__385.0_______6,737.50
20-under 25 35___22.5__787.5_______17,718.75
25-under 30 29___27.5__797.5_______21,931.25
30-under 35 16___32.5__520.0_______16,900.00
35-under 40 8____37.5__300.0_______11,250.00
40-under 45 4____42.5__170.0_______7,225.00
45-under 50 2____47.5__95.0________4,512.50
∑f = n = 122 ∑fM = 3,130.0 ∑fM2 = 87,212.50
S = √57.11 = 7.56
The sample variance is 57.11 and the standard deviation is 7.56.
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