Answer:

Range = maximum value – minimum value

Range = 8 – 3

Range = 5

Average Deviation = (|3-5| + |4-5| + |5-5| + |5-5| + |6-5| + |7-5| + |7-5| + |7-5| + |8-5| + |8-5|)/10

Average Deviation = 7/10

Average Deviation = 0.7

Variance = Σ(xi – x̄)^2 / n

Where,

Σ = summation

xi = ith value in the dataset

x̄ = mean or average of the dataset

n = total number of values in the dataset

x̄ = (3 + 4 + 5 + 5 + 6 + 7 + 7 + 7 + 8 + 8) / 10

x̄ = 6

Variance = [(3 - 6)^2 + (4 - 6)^2 + (5 - 6)^2 + (5 - 6)^2 + (6 - 6)^2 + (7 - 6)^2 + (7 - 6)^2 + (7 - 6)^2 + (8 - 6)^2 + (8 - 6)^2] / 10

Variance = (9 + 4 + 1 + 1 + 0 + 1 + 1 + 1 + 4 + 4) / 10

Variance = 2.3

Standard Deviation = √Variance

Standard Deviation = √2.3

Standard Deviation = 1.516

Answer:

Range:

The range is the difference between the highest and lowest values in a set of observations.

Range = highest value - lowest value

Range = 8 - 3

Range = 5

Average Deviation:

The average deviation is the average of the absolute deviations from the mean.

First, we need to calculate the mean of the set of observations.

Mean = (3+4+5+5+6+7+7+7+8+8)/10

Mean = 6

Then, we calculate the absolute deviations from the mean and sum them up.

|3-6| + |4-6| + |5-6| + |5-6| + |6-6| + |7-6| + |7-6| + |7-6| + |8-6| + |8-6| = 10

Average Deviation = 10/10

Average Deviation = 1

Variance:

Variance is the average of the squared deviations from the mean.

First, we need to calculate the mean of the set of observations.

Mean = (3+4+5+5+6+7+7+7+8+8)/10

Mean = 6

Then, we calculate the deviations from the mean, square them, and sum them up.

(3-6)^2 + (4-6)^2 + (5-6)^2 + (5-6)^2 + (6-6)^2 + (7-6)^2 + (7-6)^2 + (7-6)^2 + (8-6)^2 + (8-6)^2 = 30

Variance = 30/10

Variance = 3

Standard Deviation:

The standard deviation is the square root of the variance.

Standard Deviation = sqrt(3)

Standard Deviation = 1.73 (approx)