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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.

Other Sample Assignments in Statistics Homework Assignment :

Continious Distribution	Descrete Distributions
Descriptive Statistics	Nonparamatric Statistics
Probability	Sampling And Sampling Distribution
Statistical Inference Estimation For Single Popula	Simple Regression Analysis
Statistical Inference About 2 Population	Time Series Forcasting Index Number
Statistical Quality Control	Correlation
Index Number	Larger Sample Mean Proportions
Non Parametric Test	Probability Theory
Sampling Distribution	Simple and Multiple Linear Regression Analysis
Unvariate Analysis

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