Assignment Bum Mathematics 20-2 Module 4 3. The table below lists the resting heart rate for a group of Grade 11 students. \begin{tabular}{|c|c|} \hline $\begin{array}{c}\text { Heart Rate } \\ \text { (Beats per } \\ \text { Minute) }\end{array}$ & $\begin{array}{c}\text { Frequency } \\ \text { (Number of } \\ \text { students) }\end{array}$ \\ \hline $44-48$ & 5 \\ \hline $48-52$ & 7 \\ \hline $52-56$ & 10 \\ \hline $56-60$ & 12 \\ \hline $60-64$ & 8 \\ \hline $64-68$ & 8 \\ \hline $68-72$ & 6 \\ \hline $72-76$ & 1 \\ \hline \end{tabular} a. Find the mean and standard deviation for the data. b. The group of students all decide to increase their daily physical activity. What do you expect to happen to the mean and standard deviation of the heart rates? (you may need to research online what the effect being more healthy does to the heart rate) Page $8 / 15$

Step 1 ：First, calculate the midpoint of each interval, which is the average of the lower and upper bounds. The intervals and their midpoints are as follows: \((44, 48)\) with midpoint 46.0, \((48, 52)\) with midpoint 50.0, \((52, 56)\) with midpoint 54.0, \((56, 60)\) with midpoint 58.0, \((60, 64)\) with midpoint 62.0, \((64, 68)\) with midpoint 66.0, \((68, 72)\) with midpoint 70.0, and \((72, 76)\) with midpoint 74.0.

Step 2 ：Next, multiply each midpoint by its corresponding frequency to get the total for each interval. The frequencies and their totals are as follows: 5 with total 230.0, 7 with total 350.0, 10 with total 540.0, 12 with total 696.0, 8 with total 496.0, 8 with total 528.0, 6 with total 420.0, and 1 with total 74.0.

Step 3 ：Then, calculate the mean by dividing the sum of these totals by the sum of the frequencies. The mean is approximately 58.49 beats per minute.

Step 4 ：To find the standard deviation, first calculate the variance. This involves subtracting the mean from each midpoint, squaring the result, and multiplying by the corresponding frequency. The sum of these products divided by the sum of the frequencies gives the variance, which is approximately 53.93.

Step 5 ：Finally, calculate the standard deviation by taking the square root of the variance. The standard deviation is approximately 7.34 beats per minute.

Step 6 ：The mean resting heart rate for the group of Grade 11 students is approximately \(\boxed{58.49}\) beats per minute, and the standard deviation is approximately \(\boxed{7.34}\) beats per minute.