To calculate the sum of squares (SS) using the given set of scores $1, 2, 4, 4, 5$, we follow these steps:

Step 1: Calculate the mean ($\mu$)

The mean is the average of all the values: $\mu = \frac{1 + 2 + 4 + 4 + 5}{5} = \frac{16}{5} = 3.2$

Step 2: Subtract the mean from each score (Deviation from the mean)

Now subtract the mean ($\mu = 3.2$) from each value:

• $1 - 3.2 = -2.2$
• $2 - 3.2 = -1.2$
• $4 - 3.2 = 0.8$
• $4 - 3.2 = 0.8$
• $5 - 3.2 = 1.8$

Step 3: Square each deviation

Next, square each of the deviations calculated in step 2:

• $(-2.2)^2 = 4.84$
• $(-1.2)^2 = 1.44$
• $(0.8)^2 = 0.64$
• $(0.8)^2 = 0.64$
• $(1.8)^2 = 3.24$

Step 4: Sum of squares (SS)

Now, add all the squared deviations together to get the sum of squares (SS): $SS = 4.84 + 1.44 + 0.64 + 0.64 + 3.24 = 10.8$

So, the sum of squares (SS) for this set of scores is 10.8.

Would you like further explanation on any step?

Here are some related questions you might find interesting:

1. What is the variance for this dataset?
2. How do you compute the standard deviation from the sum of squares?
3. What is the relationship between variance and sum of squares?
4. How does changing one value affect the sum of squares?
5. How do we calculate SS for larger datasets?

Tip: The sum of squares is a key concept used to measure the spread of a dataset in statistics!