Question

evan, a candy store employee, placed peppermint candies into jars of various sizes.

number of peppermint candies	number of jars
33	1
38	2
80	3
181	3

x is the number of peppermint candies that a randomly chosen jar had. what is the standard deviation of x?
round your answer to the nearest hundredth.

Explanation:

Step1: Calculate the total number of jars

$n=1 + 1+2 + 3+3=10$

Step2: Calculate the mean $\mu$

$\mu=\frac{0\times1 + 33\times1+38\times2 + 80\times3+181\times3}{10}=\frac{0 + 33+76+240+543}{10}=\frac{992}{10}=99.2$

Step3: Calculate the squared - differences and multiply by frequencies

$(0 - 99.2)^2\times1=9840.64$
$(33 - 99.2)^2\times1=( - 66.2)^2\times1 = 4382.44$
$(38 - 99.2)^2\times2=( - 61.2)^2\times2=3745.44\times2 = 7490.88$
$(80 - 99.2)^2\times3=( - 19.2)^2\times3=368.64\times3 = 1105.92$
$(181 - 99.2)^2\times3=(81.8)^2\times3=6691.24\times3 = 20073.72$

Step4: Sum up the values from Step3

$S=9840.64+4382.44 + 7490.88+1105.92+20073.72=42893.6$

Step5: Calculate the variance $\sigma^{2}$

$\sigma^{2}=\frac{S}{n}=\frac{42893.6}{10}=4289.36$

Step6: Calculate the standard deviation $\sigma$

$\sigma=\sqrt{4289.36}\approx65.49$

Answer:

$65.49$