Calculate the Mean, Median, Variance, Standard Deviation, Coefficient of Variation

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Examlex · Accepted Answer

The Answer is To calculate the mean, median, variance, standard deviation, coefficient of variation, and interquartile range for the given data set (9, 13, 14, 16, 17, 21), we can follow these steps:

Mean:
Mean = (9 + 13 + 14 + 16 + 17 + 21) / 6
Mean = 90 / 6
Mean = 15

Median:
Since the data set has an even number of values, the median is the average of the two middle numbers.
Median = (14 + 16) / 2
Median = 15

Variance:
Variance = Σ(xi - μ)² / n
Where Σ represents the sum, xi represents each individual value, μ represents the mean, and n represents the number of values.
Variance = ((9-15)² + (13-15)² + (14-15)² + (16-15)² + (17-15)² + (21-15)²) / 6
Variance = (36 + 4 + 1 + 1 + 4 + 36) / 6
Variance = 82 / 6
Variance = 13.67

Standard Deviation:
Standard Deviation = √Variance
Standard Deviation = √13.67
Standard Deviation ≈ 3.7

Coefficient of Variation:
Coefficient of Variation = (Standard Deviation / Mean) * 100
Coefficient of Variation = (3.7 / 15) * 100
Coefficient of Variation ≈ 24.67%

Interquartile Range:
To find the interquartile range, we first need to find the first quartile (Q1) and the third quartile (Q3).
Q1 = (13 + 14) / 2
Q1 = 13.5
Q3 = (16 + 17) / 2
Q3 = 16.5
Interquartile Range = Q3 - Q1
Interquartile Range = 16.5 - 13.5
Interquartile Range = 3

So, the mean is 15, the median is 15, the variance is 13.67, the standard deviation is approximately 3.7, the coefficient of variation is approximately 24.67%, and the interquartile range is 3 for the given data set.

Calculate the Mean, Median, Variance, Standard Deviation, Coefficient of Variation

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