Chapter 3.1, Problem 44E

(a)

To determine

To Find: the mean and median Google stock closing price in May.

Answer to Problem 44E

Prices for Google stock for each day of trading in May, mean price $\approx 872.5$ and median price $=876.02$

Explanation of Solution

Given:

  $\begin{array}{l}845.72,857.23,861.55,868.31,870.76,871.22,871.48,873.32,873.63,877.53,\\ 880.23,881.27,882.79,887.10,889.42,903.87,906.97,908.53,909.18,915.89\end{array}$

Formula Used:

  $\begin{array}{l}\text{Mean}(\overline{x})=\frac{{\displaystyle \sum x_i}}{n}\\ \\ \text{Median}=\left\{\begin{array}{l}\frac{{\left(n+1\right)}^{\text{th }}\text{term}}{2},\text{When}\text{n}\text{is}\text{odd}\\ \frac{{\left(\frac{n}{2}+1\right)}^{\text{th }}\text{term + }{\left(\frac{n}{2}\right)}^{\text{th}}\text{term}}{2},\text{When n is even}\end{array}\right\}\end{array}$

Calculation- Mean and Median prices for Google stock for each day of trading in May,

  $\begin{array}{c}\overline{x}=\frac{\sum x_i}{n}\\ =\frac{\left[\begin{array}{l}880.37+877.07+873.65+866.00+869.79+829.61+880.93+884.74+900.68+900.62+886.25+\\ 820.43+875.04+877.00+871.98+879.81+890.22+879.73+864.64+859.70+859.10+867.63\end{array}\right]}{22}\\ =\frac{19194}{22}\\ =872.5\end{array}$

For Median, arrange data in sequential order,

  $\begin{array}{l}820.43,829.61,859.10,859.70,864.64,866.20,867.63,869.79,871.98,873.65,875.04,\\ 877.00,877.07,879.73,879.81,880.37,880.93,884.74,886.25,890.22,900.62,900.68\end{array}$

  $\begin{array}{c}\text{Median =}\left(\frac{{\left(\frac{\text{n}}{\text{2}}\right)}^{\text{th}}\text{term+}{\left(\frac{\text{n}}{\text{2}}\text{+1}\right)}^{\text{th}}\text{term}}{\text{2}}\right)\\ \text{=}\left(\frac{{\left(\frac{\text{22}}{\text{2}}\right)}^{\text{th}}\text{term+}{\left(\frac{\text{22}}{\text{2}}\text{+1}\right)}^{\text{th}}\text{term}}{\text{2}}\right)\\ \text{=}\left(\frac{{\left(\text{11}\right)}^{\text{th}}\text{term+}{\left(\text{12}\right)}^{\text{th}}\text{term}}{\text{2}}\right)\\ \text{=}\left(\frac{\text{875}\text{.04+877}}{\text{2}}\right)\\ \text{=}\frac{\text{1752}\text{.04}}{\text{2}}\\ \text{=876}\text{.02}\end{array}$

Therefore, Prices for Google stock for each day of trading in May, mean price $\approx 872.5$ and median price $=876.02$

(b)

To determine

To Find: the mean and median Google stock closing price in June.

Answer to Problem 44E

Prices for Google stock for each day of trading in June, mean price $=881.8$ and median price $=878.88$

Explanation of Solution

Calculation-

Mean and Median prices for Google stock for each day of trading in June,

  $\begin{array}{c}\overline{x}=\frac{\sum x_i}{n}\\ =\frac{\left[\begin{array}{l}871.22+870.76+868.31+881.27+873.32+882.79+889.42+906.97+908.53+909.18+\\ 903.87+915.89+887.10+877.53+880.23+871.48+873.63+857.23+861.55+845.72\end{array}\right]}{20}\\ =\frac{17636}{20}\\ =881.8\end{array}$

For Median, arrange data in sequential order,

  $\begin{array}{l}845.72,857.23,861.55,868.31,870.76,871.22,871.48,873.32,873.63,877.53,\\ 880.23,881.27,882.79,887.10,889.42,903.87,906.97,908.53,909.18,915.89\end{array}$

  $\begin{array}{c}\text{Median = }\left(\frac{{\left(\frac{\text{n}}{\text{2}}\right)}^{\text{th}}\text{term+}{\left(\frac{\text{n}}{\text{2}}\text{+1}\right)}^{\text{th}}\text{term}}{\text{2}}\right)\\ \text{=}\left(\frac{{\left(\frac{\text{20}}{\text{2}}\right)}^{\text{th}}\text{term+}{\left(\frac{\text{20}}{\text{2}}\text{+1}\right)}^{\text{th}}\text{term}}{\text{2}}\right)\\ \text{=}\left(\frac{{\left(\text{10}\right)}^{\text{th}}\text{term+}{\left(\text{11}\right)}^{\text{th}}\text{term}}{\text{2}}\right)\\ \text{=}\left(\frac{\text{877}\text{.53+880}\text{.23}}{\text{2}}\right)\\ \text{=}\frac{\text{1757}\text{.76}}{\text{2}}\\ \text{=878}\text{.88}\end{array}$

Therefore, Prices for Google stock for each day of trading in June, mean price $=881.8$ and median price $=878.88$

(c)

To determine

To Check: The substantial difference in price between May and June.

Answer to Problem 44E

No, there is not any substantial difference in price between May and June. The prices are almost same.

Explanation of Solution

By looking at the mean and median prices of google closing stock between May and June,

Prices for Google stock for each day of trading in May, mean price $\approx 872.5$ and median price $=876.02$

Prices for Google stock for each day of trading in June, mean price $=881.8$ and median price $=878.88$

So, it can be said that No, there is not any substantial difference in price between May and June. The prices are almost same.