Question

Given the following pairs of x, y data find SS(x) to one decimal

place. Data: (33, 14), (46, 51), (76, 5), (81, 62), (77, 17)

Answer 1

SS(x) = 3418.0 the sum of squares for the x-values is 3418.0. This value represents the variability of the x-values around their mean, indicating how much each x-value deviates from the average x-value.

Explanation:

To calculate SS(x) (the sum of squares for the x-values), use the formula:

`\[ SS(x) = \sum_(i=1)^(n) (x_i - \bar{x})^2 \]`

Where \(x_i\) represents each x-value, and \(\bar{x}\) is the mean of all x-values. The given data consists of x-values: 33, 46, 76, 81, and 77. First, find the mean of these x-values:

`\[ \bar{x} = (33 + 46 + 76 + 81 + 77)/(5) = (313)/(5) = 62.6 \]`

Then, calculate the squared differences between each x-value and the mean:

`\[ (33 - 62.6)^2 = 893.16 \]`

`\[ (46 - 62.6)^2 = 277.04 \]`

`\[ (76 - 62.6)^2 = 179.56 \]`

`\[ (81 - 62.6)^2 = 337.24 \]`

`\[ (77 - 62.6)^2 = 207.36 \]`

Finally, sum up these squared differences to obtain SS(x):

`\[ SS(x) = 893.16 + 277.04 + 179.56 + 337.24 + 207.36 = 1894.36 + 1523.6 = 3418.0 \]`

Therefore, the sum of squares for the x-values is 3418.0. This value represents the variability of the x-values around their mean, indicating how much each x-value deviates from the average x-value. This calculation aids in understanding the dispersion or spread of the x-values in the dataset.

Answer 2

SS(x) = 3306.0. The sum of squares for the variable x (SS(x)) based on the provided data set is 3306.0. This value represents the sum of the squared deviations of x-values from their mean.

Explanation:

To find the sum of squares for the variable x (SS(x)), follow these steps:

1. Compute the mean (average) of the x-values.

2. Find the deviation of each x-value from the mean.

3. Square each deviation.

4. Add up all the squared deviations to get SS(x).

Explanation:

1. Calculate the mean of the x-values:

Mean = (33 + 46 + 76 + 81 + 77) / 5

= 313 / 5

= 62.6

2. Find the deviation of each x-value from the mean:

Deviation for (33, 14): 33 - 62.6 = -29.6

Deviation for (46, 51): 46 - 62.6 = -16.6

Deviation for (76, 5): 76 - 62.6 = 13.4

Deviation for (81, 62): 81 - 62.6 = 18.4

Deviation for (77, 17): 77 - 62.6 = 14.4

3. Square each deviation:

(-29.6)^2 ≈ 873.6

(-16.6)^2 ≈ 275.6

(13.4)^2 ≈ 179.6

(18.4)^2 ≈ 338.6

(14.4)^2 ≈ 207.4

4. Sum up the squared deviations to find SS(x):

SS(x) = 873.6 + 275.6 + 179.6 + 338.6 + 207.4

≈ 1874.8 + 545.8 + 545.8

≈ 3306.0