Complete the following statements. In general, $\%$ of the values in a data set lie at or below the $56^{\text {th }}$ percentile. $\%$ of the values in a data set lie at or above the $70^{\text {th }}$ percentile.. If a sample consists of 800 test scores, of them would be at or below the $20^{\text {th }}$ percentile. If a sample consists of 800 test scores, of them would be at or above the $30^{\text {th }}$ percentile.

Step 1 ：The percentile of a value in a data set is the percentage of values in the data set that are less than or equal to that value. So, if a value is at the 56th percentile, it means that 56% of the values in the data set are less than or equal to that value. Similarly, if a value is at the 70th percentile, it means that 70% of the values in the data set are less than or equal to that value. Therefore, 100 - 70 = 30% of the values are greater than or equal to that value.

Step 2 ：For the third and fourth questions, we need to calculate the number of test scores that are at or below the 20th percentile and at or above the 30th percentile respectively. This can be done by multiplying the total number of test scores by the respective percentile (expressed as a decimal).

Step 3 ：Final Answer: \(\boxed{56\%}\) of the values in a data set lie at or below the 56th percentile.

Step 4 ：Final Answer: \(\boxed{30\%}\) of the values in a data set lie at or above the 70th percentile.

Step 5 ：Final Answer: If a sample consists of 800 test scores, \(\boxed{160}\) of them would be at or below the 20th percentile.

Step 6 ：Final Answer: If a sample consists of 800 test scores, \(\boxed{560}\) of them would be at or above the 30th percentile.