Question

1. the dot plot displays the number of marshmallows added to hot cocoa by several kids. which is the standard deviation of the data represented in the dot plot? a. 0.2 marshmallow b. 1 marshmallow c. 2 marshmallows d. 5 marshmallows

Explanation:

Step1: Count data - point frequencies

Let's assume the frequencies of the data - points from left to right. The value 3 has 1 dot, the value 4 has 1 dot, the value 5 has 5 dots, the value 6 has 1 dot, and the value 7 has 1 dot. So the data set is {3, 4, 5, 5, 5, 5, 5, 6, 7} and \(n = 9\).

Step2: Calculate the mean \(\bar{x}\)

\(\bar{x}=\frac{3 + 4+5\times5 + 6+7}{9}=\frac{3 + 4+25 + 6+7}{9}=\frac{45}{9}=5\)

Step3: Calculate the squared - differences

\((3 - 5)^2=4\), \((4 - 5)^2 = 1\), \((5 - 5)^2=0\) (five times), \((6 - 5)^2 = 1\), \((7 - 5)^2=4\)

Step4: Calculate the variance \(s^{2}\)

\(s^{2}=\frac{4 + 1+0\times5 + 1+4}{9}=\frac{10}{9}\approx1.11\)

Step5: Calculate the standard deviation \(s\)

\(s=\sqrt{s^{2}}=\sqrt{\frac{10}{9}}\approx1.05\approx1\)

Answer:

b. 1 marshmallow