Based on the calculations, the two (2) statements which are true are:
Mathematically, range can be calculated by using this formula;
Range = Highest number - Lowest number
Range 1 = 71 - 32
Range 1 = 39.
Range 2 = 71 - 3
Range 2 = 68.
Therefore, the range of Data Set 2 is not smaller than the range of Data Set 1.
Mathematically, the mean for these data sets would be calculated by using this formula:
Mean = [F(x)]/n
For the total number of Data Set 1, we have:
F(x) = 32 + 41 + 51 + 63 + 66 + 71
F(x) = 324.
Substituting the parameters into the formula, we have:
Mean = [F(x)]/n
Mean 1 = [324]/6
Mean 1 = 54.
For the total number of Data Set 2, we have:
F(x) = 32 + 41 + 51 + 3 + 66 + 71
F(x) = 324.
Substituting the parameters into the formula, we have:
Mean 2 = [264]/6
Mean 2 = 44.
Difference = Mean 1 - Mean 2
Difference = 54 - 44
Difference = 10.
Therefore, the mean of Data Set 2 is exactly 10 less than the mean of Data Set 1.
For the standard deviation of Data Set 1, we have:
SD₁ = √(1/n × ∑(xi - u₁)²)
SD₁ = √(1/5 × ∑(32 - 54)² + 1/5 × ∑(41 - 54)² + 1/5 × ∑(51 - 54)² + 1/5 × ∑(63 - 54)² + 1/5 × ∑(66 - 54)² + 1/5 × ∑(71 - 54)²)
SD₁ = 15.34.
For the standard deviation of Data Set 2, we have:
SD₂ = √(1/n × ∑(xi - u₂)²)
SD₂ = √(1/5 × ∑(32 - 44)² + 1/5 × ∑(41 - 44)² + 1/5 × ∑(51 - 44)² + 1/5 × ∑(3 - 44)² + 1/5 × ∑(66 - 44)² + 1/5 × ∑(71 - 44)²)
SD₂ = 24.88.
Therefore, the standard deviation of Data Set 2 is larger than the standard deviation of Data Set 1.
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