Variance - the measure of dispersion that accounts for the average squared deviation of each observation from the mean. Since we square the difference of each observation from the mean, the unit of measurement of the variance is the square of the unit used in measuring each observation. 0² = Σ(1₁-1)² N Example 1. Consider the following scores of 5 students in their Statistics Exam. Compute the variance. Student 1 2 3 4 5 Score (x) 38 50 49 35 45 Step 1: Compute the mean 38+50 +49 +35+45 x= 5 217 5 x = 43.4 Step 2: Compute the variance Σ(x₁ - x)² 0² = N (38-43.4)² + (50 — 43.4)² + (49 — 43.4)² + (35 − 43.4)² + (45 − 43.4)² 0² = 5 29.16+43.56 +31.36+70.56 +2.56 0² = 5 177.2 5 a²=35.44 Exercise: Compute the variance of the following data set Day 1 2 3 4 5 Allowance (x) 50 60 45 60 40

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Variance - the measure of dispersion that accounts for the average squared deviation of each
observation from the mean. Since we square the difference of each observation from the mean,
the unit of measurement of the variance is the square of the unit used in measuring each
observation.
Σ,(x − 1)
0² =
N
Example 1. Consider the following scores of 5 students in their Statistics Exam. Compute the
variance.
Student 1 2 3 4 5
Score (x) 38 50 49 35 45
Step 1: Compute the mean
38 +50 +49 +35+45
x=
5
x=
217
5
x = 43.4
Step 2: Compute the variance
Σ(x₁ - x)²
0² =
N
(38-43.4)² + (50-43.4)²+(49− 43.4)² + (35 − 43.4)² + (45 − 43.4)²
0² =
5
29.16+43.56 +31.36+70.56 +2.56
a² =
5
0² =
177.2
5
a² = 35.44
Exercise: Compute the variance of the following data set
Day
1 2 3 4 5
Allowance (x) 50 60 45 60 40
Transcribed Image Text:Variance - the measure of dispersion that accounts for the average squared deviation of each observation from the mean. Since we square the difference of each observation from the mean, the unit of measurement of the variance is the square of the unit used in measuring each observation. Σ,(x − 1) 0² = N Example 1. Consider the following scores of 5 students in their Statistics Exam. Compute the variance. Student 1 2 3 4 5 Score (x) 38 50 49 35 45 Step 1: Compute the mean 38 +50 +49 +35+45 x= 5 x= 217 5 x = 43.4 Step 2: Compute the variance Σ(x₁ - x)² 0² = N (38-43.4)² + (50-43.4)²+(49− 43.4)² + (35 − 43.4)² + (45 − 43.4)² 0² = 5 29.16+43.56 +31.36+70.56 +2.56 a² = 5 0² = 177.2 5 a² = 35.44 Exercise: Compute the variance of the following data set Day 1 2 3 4 5 Allowance (x) 50 60 45 60 40
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