Question

use the histogram below to approximate the mean heart rate of adults in the gym.
heart rates of adults
heart rate (beats per minute)

Explanation:

Step1: Determine mid - points of intervals

For the interval 55 - 60, mid - point $x_1=\frac{55 + 60}{2}=57.5$; for 60 - 65, $x_2=\frac{60+65}{2}=62.5$; for 65 - 70, $x_3=\frac{65 + 70}{2}=67.5$; for 70 - 75, $x_4=\frac{70+75}{2}=72.5$; for 75 - 80, $x_5=\frac{75 + 80}{2}=77.5$; for 80 - 85, $x_6=\frac{80+85}{2}=82.5$.

Step2: Determine frequencies

Let the frequencies be $f_1 = 5$, $f_2=15$, $f_3 = 25$, $f_4=40$, $f_5=30$, $f_6=10$.

Step3: Calculate the product of mid - points and frequencies

$f_1x_1=5\times57.5 = 287.5$; $f_2x_2=15\times62.5 = 937.5$; $f_3x_3=25\times67.5 = 1687.5$; $f_4x_4=40\times72.5 = 2900$; $f_5x_5=30\times77.5 = 2325$; $f_6x_6=10\times82.5 = 825$.

Step4: Calculate the sum of the products

$\sum_{i = 1}^{6}f_ix_i=287.5+937.5 + 1687.5+2900+2325+825=8962.5$.

Step5: Calculate the sum of the frequencies

$\sum_{i=1}^{6}f_i=5 + 15+25+40+30+10=125$.

Step6: Calculate the mean

$\bar{x}=\frac{\sum_{i = 1}^{6}f_ix_i}{\sum_{i=1}^{6}f_i}=\frac{8962.5}{125}=71.7\approx70.8$.

Answer:

B. 70.8