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Use the following table to compute the standard deviation, variance and range of the data values.

ix₁xx₁ - x (x₁ - x)²
1 12 9
3
9
299
0
0
369
Your answers will be exact numerical values.
The standard deviation is
The variance is
The range is
-3
9

User BWS
by
8.8k points

1 Answer

1 vote

Explanation:

Step 1: Find the mean x of the data values.

X = (ix₁) / n

x = (12 + 3 + 9 + 2 + 0 + 0 + 3) / 7

x = 29 / 7

x ≈ 4.14 (rounded to two decimal places)

Step 2: Calculate the squared differences from the mean for each data value [(x₁ - x)²].

For each data value, subtract the mean and square the result.

Squared Differences:

(12 - 4.14)² ≈ 53.43

(3 - 4.14)² ≈ 1.31

(9 - 4.14)² ≈ 23.09

(2 - 4.14)² ≈ 4.34

(0 - 4.14)² ≈ 17.11

(0 - 4.14)² ≈ 17.11

(3 - 4.14)² ≈ 1.31

Step 3: Calculate the variance (s²) of the data values.

s² = ((x₁ - x)²) / (n - 1)

s² = (53.43 + 1.31 + 23.09 + 4.34 + 17.11 + 17.11 + 1.31) / (7 - 1)

s² ≈ 117.70 / 6

s² ≈ 19.62 (rounded to two decimal places)

Step 4: Calculate the standard deviation (s) of the data values.

s = √s²

s = √19.62

s ≈ 4.43 (rounded to two decimal places)

Step 5: Find the range of the data values.

Range = Maximum value - Minimum value

Range = 12 - 0

Range = 12

Therefore, the results are:

The standard deviation is approximately 4.43 (rounded to two decimal places).

The variance is approximately 19.62 (rounded to two decimal places).

The range is 12.

User Matt Catellier
by
8.7k points