Answer:
The mean, the mode , the standard deviation and the variance.
Step-by-step explanation:
The measure of central tendency we use here is the mean and the dispersion its variance. Now, the mean is given by x =∑x₁/n where x₁ is the individual value and n the total number of values. Let p be the sum of the other nine number excluding the last number which is either 16 or 18. The sum of the ten numbers including 16 is q = p + 16 and the mean of these number μ₁ = ∑x/n = q/n = (p + 16)/n= p/n + 16/n. Let r be the sum of the ten numbers including 18. So, r = p + 18. The mean of these number μ₂ = ∑x/n = r/n = (p + 18)/n= p/n + 18/n. Since n = 10, μ₁ = p/10 + 1.6 and μ₂ = p/10 + 1.8.
p = 4 + 5 + 8 + 9 + 11 + 13 + 15 + 18 + 18 + 20 = 103. So, μ₁ = p/10 + 1.6 = 103/10 + 1.6 = 11.9 and μ₂ = p/10 + 1.8 = 103/10 + 1.8 = 12.1 .So, the mean are different.
We now check if the variance is σ² = ∑(x₁ - μ)²/n. We now compute the variance for the two set of data. σ₁ and μ₁ are original variance and mean, while σ₂ and μ₂ are final variance and mean. σ²₁ = [(4 - 12.1)² + (5 - 12.1)² + (8 - 12.1)² + (9 - 12.1)² + (11 - 12.1)² + (13 - 12.1)² + (15 - 12.1)² + (18 - 12.1)² + (18 - 12.1)² + (20 - 12.1)²]/10 = [65.61 + 50.41 + 16.81 + 9.61 + 1.21 + 0.81 + 8.41 + 34.81 + 34.81 + 62.41]/10 = 284.9/10 = 28.49
σ²₂ = [(4 - 11.9)² + (5 - 11.9)² + (8 - 11.9)² + (9 - 11.9)² + (11 - 11.9)² + (13 - 11.9)² + (15 - 11.9)² + (16 - 11.9)² + (18 - 11.9)² + (20 - 11.9)²]/10 = [62.41 + 47.61 + 15.21 + 8.41 + 0.81 + 1.21 +9.61 + 16.81 + 37.21 + 65.61]/10 = 264.9/10=26.49 . Since, σ₁² = 28,49 ≠ σ₂² = 26.49, the variance changes.
So, both the mean and the variance change from the original data. The median = (11 + 13)/2 = 24/2 = 12 remains the same. The range = 20 - 4 = 15 remains the same. The mode also changes since we now have only one 18. The standard deviation also changes since S.D = √σ² = σ. σ₁ = 5.34 and σ₂ = 5.15
