the train conductor made sure to count the number of passengers on each train.\nnumber of passengers number…

Explanation:

Step1: Calculate the total number of trains

$n=3 + 1+3 + 3=10$

Step2: Calculate the mean $\mu$

$\mu=\frac{(124\times3)+(166\times1)+(245\times3)+(262\times3)}{10}=\frac{372 + 166+735+786}{10}=\frac{2059}{10}=205.9$

Step3: Calculate the squared - differences and their weighted sum

$(124 - 205.9)^2\times3+(166 - 205.9)^2\times1+(245 - 205.9)^2\times3+(262 - 205.9)^2\times3$ $=(-81.9)^2\times3+(-39.9)^2\times1+(39.1)^2\times3+(56.1)^2\times3$ $=(6707.61\times3)+(1592.01\times1)+(1528.81\times3)+(3147.21\times3)$ $=20122.83+1592.01 + 4586.43+9441.63$ $=35742.9$

Step4: Calculate the variance $\sigma^{2}$

$\sigma^{2}=\frac{35742.9}{10}=3574.29$

Step5: Calculate the standard deviation $\sigma$

$\sigma=\sqrt{3574.29}\approx59.79$

Answer:

$59.79$