Each year advertisers spend billions of dollars purchasing commercial time on network television. In the first 6 months of one year, advertisers spent $1.1 billion. Who were the largest spenders? In a recent article, the top 10 leading spenders and how much each spent (in million of dollars) were listed: $$\begin{array} { l r l r }
\text { Company A } & \$ 71.4 & \text { Company F } & \$ 27.1 \
\text { Company B } & 60.1 & \text { Company G } & 25.1 \
\text { Company C } & 56.5 & \text { Company H } & 23.1 \
\text { Company D } & 55 & \text { Company I } & 22.9 \
\text { Company E } & 28.6 & \text { Company J } & 20.6
\end{array}$$ Calculate the sample variance.
A) 372.307
B) 3759.244
C) 2070.113
D) 1854.860

Question

Each year advertisers spend billions of dollars purchasing commercial time on network television. In the first 6 months of one year, advertisers spent $1.1 billion. Who were the largest spenders? In a recent article, the top 10 leading spenders and how much each spent (in million of dollars) were listed: $$\begin{array} { l r l r } 
\text { Company A } & \$ 71.4 & \text { Company F } & \$ 27.1 \
\text { Company B } & 60.1 & \text { Company G } & 25.1 \
\text { Company C } & 56.5 & \text { Company H } & 23.1 \
\text { Company D } & 55 & \text { Company I } & 22.9 \
\text { Company E } & 28.6 & \text { Company J } & 20.6
\end{array}$$ Calculate the sample variance.
A) 372.307
B) 3759.244
C) 2070.113
D) 1854.860

Quizplus · Accepted Answer

The sample variance is calculated as the sum of the squared deviations from the mean divided by the number of observations minus one. The mean is calculated as the sum of the observations divided by the number of observations. In this case, the mean is (71.4 + 60.1 + 56.5 + 55 + 28.6 + 27.1 + 25.1 + 23.1 + 22.9 + 20.6) / 10 = 440.4 / 10 = 44.04. The squared deviations from the mean are (71.4 - 44.04)^2 + (60.1 - 44.04)^2 + (56.5 - 44.04)^2 + (55 - 44.04)^2 + (28.6 - 44.04)^2 + (27.1 - 44.04)^2 + (25.1 - 44.04)^2 + (23.1 - 44.04)^2 + (22.9 - 44.04)^2 + (20.6 - 44.04)^2 = 1854.86. The sample variance is therefore 1854.86 / (10 - 1) = 1854.86 / 9 = 206.118.

Each Year Advertisers Spend Billions of Dollars Purchasing Commercial Time