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Zorluk: OrtaMeasures of Dispersion

A football coach records the number of goals scored by a team in six consecutive matches as 1,3,4,6,7,1, 3, 4, 6, 7, and 99. What is the variance of the goals scored?

Cevap: 7

Cevap

The variance of the goals scored is 7.
To find the variance of the goals scored, first calculate the mean: xˉ=1+3+4+6+7+96=306=5\bar{x} = \frac{1+3+4+6+7+9}{6} = \frac{30}{6} = 5. Next, determine the sum of the squared deviations from the mean: (1−5)2+(3−5)2+(4−5)2+(6−5)2+(7−5)2+(9−5)2=16+4+1+1+4+16=42(1-5)^2 + (3-5)^2 + (4-5)^2 + (6-5)^2 + (7-5)^2 + (9-5)^2 = 16 + 4 + 1 + 1 + 4 + 16 = 42. Dividing this total by the number of data values (N=6N = 6) yields 426=7\frac{42}{6} = 7.

Adım Adım Çözüm

1
Calculate the mean of the dataset
\bar{x} = 5
The mean is needed as the reference point for computing deviations.
2
Compute the squared deviation of each data point from the mean
Squared deviations are 16, 4, 1, 1, 4, and 16
Variance measures the average squared distance from the mean.
3
Sum the squared deviations and divide by the number of observations N = 6
Variance = 7
The formula for variance of ungrouped data is \sigma^2 = \frac{\sum (x - \bar{x})^2}{N}.

Anahtar Kavram

Variance of Ungrouped Data
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Konular

Measures of Dispersion

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