B3. In the city hospital, there are 120 patients. After the morning heart rate measurement, the head nurse classified the measurements into 8 frequency classes. Calculate the arithmetic mean of the measurements and the standard deviation.

| Number of heartbeats per minute | Frequency |
| :--- | :---: |
| $60-64.9$ | 23 |
| $65-69.9$ | 16 |
| $70-74.9$ | 15 |
| $75-79.9$ | 32 |
| $80-84.9$ | 24 |
| $85-89.9$ | 6 |
| $90-94.9$ | 2 |
| $95-99.9$ | 2 |
B3. First, we calculate the class midpoints, then $\bar{x}=\frac{1}{120} \cdot(62.45 \cdot 23+67.45 \cdot 16+72.45 \cdot 15+77.45 \cdot 32+82.45 \cdot 24+87.45 \cdot 6+92.45 \cdot 2+97.45 \cdot 2)=\frac{1}{120} \cdot 8964=74.7$. Using the formula $\sigma=\sqrt{\frac{1}{120} \cdot\left(23 \cdot(74.7-62.45)^{2}+16 \cdot(74.7-67.45)^{2}+\cdots+2 \cdot(74.7-97.45)^{2}\right)}=8.5$ we also calculate the standard deviation.

Calculated class midpoints...........................................................................................................

Knowledge of the formula for the arithmetic mean ............................................................................................................................

Result $\bar{x}=74.7$...........................................................................................................................

Knowledge of the formula for the standard deviation .......................................................................................................................

Procedure . ................................................................................................................................................

![](https://cdn.mathpix.com/cropped/2024_06_07_ce887fced8b2a2bf0894g-16.jpg?height=54&width=1641&top_left_y=738&top_left_x=276)