an education researcher recorded the number of students at each of the schools in his county.\n\n|number of…

an education researcher recorded the number of students at each of the schools in his county.\n\n|number of students|number of schools|\n|----|----|\n|113|2|\n|164|1|\n|384|2|\n|877|4|\n|920|1|\n\nx is the number of students that a randomly chosen school has. what is the standard deviation of x?\n\nround your answer to the nearest hundredth.

an education researcher recorded the number of students at each of the schools in his county.\n\n|number of students|number of schools|\n|----|----|\n|113|2|\n|164|1|\n|384|2|\n|877|4|\n|920|1|\n\nx is the number of students that a randomly chosen school has. what is the standard deviation of x?\n\nround your answer to the nearest hundredth.

Answer

Explanation:

Step1: Calculate the total number of schools

$n=2 + 1+2 + 4+1=10$

Step2: Calculate the mean $\mu$

$\mu=\frac{(113\times2)+(164\times1)+(384\times2)+(877\times4)+(920\times1)}{10}=\frac{226 + 164+768+3508+920}{10}=\frac{5586}{10}=558.6$

Step3: Calculate the squared - differences and their weighted sum

$(113 - 558.6)^2\times2+(164 - 558.6)^2\times1+(384 - 558.6)^2\times2+(877 - 558.6)^2\times4+(920 - 558.6)^2\times1$ $=( - 445.6)^2\times2+( - 394.6)^2\times1+( - 174.6)^2\times2+(318.4)^2\times4+(361.4)^2\times1$ $=(198569.36\times2)+(155609.16\times1)+(30485.16\times2)+(101378.56\times4)+(130609.96\times1)$ $=397138.72+155609.16 + 60970.32+405514.24+130609.96$ $=1150842.4$

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

$\sigma^{2}=\frac{1150842.4}{10}=115084.24$

Step5: Calculate the standard deviation $\sigma$

$\sigma=\sqrt{115084.24}\approx339.24$

Answer:

$339.24$