Create a data set of 7 numbers with a mean of 20, a median of 15 and a mode of 10.

To create a data set with a mean of 20, a median of 15, and a mode of 10, we can start by placing these specific values in the dataset. Let's denote the 7 numbers in the dataset as $a$ through $g$.

Given:
Mean = 20
Median = 15
Mode = 10

Step 1: Set up the data set

$a, b, c, 10, d, e, f$

Step 2: Find the mean

The mean of the data set can be calculated using the formula:
\text{Mean} = \frac{a + b + c + 10 + d + e + f}{7} = 20

a + b + c + d + e + f = 140 - 10

a + b + c + d + e + f = 130

Step 3: Find the median

Since we want the median to be 15 and the data set has 7 numbers, the 4th number in the ordered data set should be 15.

So, the ordered data set is:
$10, a, b, 15, c, d, e$

Step 4: Find the mode

Since the mode is 10, we already have one 10 in the data set.

Step 5: Solve for the missing values

From the mean calculation, we have:
a + b + c + d + e + f = 130

We can assign values to the variables to satisfy all the conditions:
$a = 5, b = 10, c = 15, d = 20, e = 25, f = 55$

So, the data set is:
$5, 10, 15, 10, 20, 25, 55$

\boxed{5, 10, 15, 10, 20, 25, 55} is the data set with the mean of 20, median of 15, and mode of 10.