A sample of 100 clients of an exercise facility was selected. Let $X=$ the number of days per week that a randomly selected client use the exercise facility.
\begin{tabular}{|c|c|}
\hline $\boldsymbol{X}$ & Frequency \\
\hline 0 & 3 \\
\hline 1 & 15 \\
\hline 2 & 30 \\
\hline 3 & 29 \\
\hline 4 & 11 \\
\hline 5 & 7 \\
\hline 6 & 5 \\
\hline
\end{tabular}

Find the number that is 1.5 standard deviations BELOW the mean. (Round your answer to three decimal places.)
\[
0.851
\]

Step 1 ：First, we need to calculate the mean of the data. The mean can be calculated by multiplying each value of X by its frequency, summing these products, and then dividing by the total number of observations.

Step 2 ：Next, we need to calculate the standard deviation of the data. This can be done by first finding the variance, which is the average of the squared differences from the Mean, and then taking the square root of the variance.

Step 3 ：Once we have the mean and standard deviation, we can find the number that is 1.5 standard deviations below the mean by subtracting 1.5 times the standard deviation from the mean.

Step 4 ：Given the values X = [0 1 2 3 4 5 6] and their corresponding frequencies freq = [ 3 15 30 29 11 7 5], we calculate the mean to be 2.71, the variance to be 1.9259, and the standard deviation to be approximately 1.388.

Step 5 ：Subtracting 1.5 times the standard deviation from the mean gives us a value of approximately 0.628.

Step 6 ：Final Answer: The number that is 1.5 standard deviations below the mean is \( \boxed{0.628} \).