To find $\text{SSTOT}$ (the total sum of squares), we need to follow these steps:

1. Calculate the overall mean $\bar{X}$ of all the data points.
2. Compute the total sum of squares $\text{SSTOT}$, which is the sum of the squared differences between each data point and the overall mean.

Let's break this down.

Step 1: Calculate the overall mean ($\bar{X}$)

We are given 22 data points for profits per employee (in thousands of dollars):

• Computers: 27.4, 23.3, 14.3, 8.2, 11.7
• Aerospace: 13.8, 9.7, 11.9, 8.8, 6.2, 19.4
• Heavy Equipment: 22.2, 20.3, 7.7, 12.6, 7.5
• Broadcasting: 17.2, 16.8, 14.1, 15.8, 10.4, 9.5

First, we calculate the sum of all data points:

$\text{Sum of all values} = 27.4 + 23.3 + 14.3 + 8.2 + 11.7 + 13.8 + 9.7 + 11.9 + 8.8 + 6.2 + 19.4 + 22.2 + 20.3 + 7.7 + 12.6 + 7.5 + 17.2 + 16.8 + 14.1 + 15.8 + 10.4 + 9.5$

Summing these values gives:

$\text{Sum} = 308.9$

Now, we calculate the overall mean $\bar{X}$:

$\bar{X} = \frac{308.9}{22} = 14.041$

Step 2: Compute SSTOT

The formula for SSTOT is:

$\text{SSTOT} = \sum (X_i - \bar{X})^2$

Where $X_i$ is each individual data point, and $\bar{X} = 14.041$.

We now subtract $\bar{X}$ from each data point, square the result, and sum them all:

$\text{SSTOT} = (27.4 - 14.041)^2 + (23.3 - 14.041)^2 + \dots + (9.5 - 14.041)^2$

Let's calculate each term:

• $(27.4 - 14.041)^2 = 176.93$
• $(23.3 - 14.041)^2 = 85.53$
• $(14.3 - 14.041)^2 = 0.07$
• $(8.2 - 14.041)^2 = 34.11$
• $(11.7 - 14.041)^2 = 5.49$
• $(13.8 - 14.041)^2 = 0.06$
• $(9.7 - 14.041)^2 = 18.79$
• $(11.9 - 14.041)^2 = 4.59$
• $(8.8 - 14.041)^2 = 27.44$
• $(6.2 - 14.041)^2 = 61.62$
• $(19.4 - 14.041)^2 = 28.67$
• $(22.2 - 14.041)^2 = 66.83$
• $(20.3 - 14.041)^2 = 39.27$
• $(7.7 - 14.041)^2 = 40.24$
• $(12.6 - 14.041)^2 = 2.08$
• $(7.5 - 14.041)^2 = 42.88$
• $(17.2 - 14.041)^2 = 9.98$
• $(16.8 - 14.041)^2 = 7.58$
• $(14.1 - 14.041)^2 = 0.00$
• $(15.8 - 14.041)^2 = 3.09$
• $(10.4 - 14.041)^2 = 13.28$
• $(9.5 - 14.041)^2 = 20.73$

Now, summing all these squared differences:

$\text{SSTOT} = 708.25$

Final Answer:

$\boxed{\text{SSTOT} = 708.250}$

Do you want further details or have any questions?

Here are five related questions to expand on this topic:

1. How do we interpret the SSTOT value in terms of variance?
2. What is the next step in an ANOVA calculation after finding SSTOT?
3. How is the overall mean different from the group-specific means?
4. How would removing an outlier affect the SSTOT?
5. What assumptions must hold for valid ANOVA results?

Tip: SSTOT helps measure total variability; higher values indicate more spread in the data.