Chapter 3.2, Problem 41E

Stock prices: Following are the closing prices of Google stock for each trading day in May and June of a recent year.

1. Find the population standard deviation for the prices in May.
2. Find the population standard deviation for the prices in June.
3. Financial analysts use the word volatility to refer to the variation in prices of assets such as stocks. In which month was the price of Google stock more volatile?

To determine

To find the Population standard deviation for prices in May.

Answer to Problem 41E

Standard Deviation = 18.53

Explanation of Solution

Given:

The data

May (Xi)	June (Yi)
880.37	871.22
877.07	870.76
873.65	868.31
866.2	881.27
869.79	873.32
829.61	882.79
880.93	889.42
884.74	906.97
900.68	908.53
900.62	909.18
886.25	903.87
820.43	915.89
875.04	887.1
877	877.53
871.98	880.23
879.81	871.48
890.22	873.63
879.73	857.23
864.64	861.55
859.7	845.72
859.1
867.63

Calculation:

	May (Xi)	${\left(x_i-\overline{x}\right)}^2$
	880.37	61.80
	877.07	20.81
	873.65	1.30
	866.2	39.80
	869.79	7.39
	829.61	1840.29
	880.93	70.92
	884.74	149.61
	900.68	793.63
	900.62	790.25
	886.25	188.83
	820.43	2712.18
	875.04	6.41
	877	20.17
	871.98	0.28
	879.81	53.31
	890.22	313.69
	879.73	52.15
	864.64	61.92
	859.7	164.06
	859.1	179.79
	867.63	23.80
SUM	19195.19	7552.38
Mean	872.51
Standard Deviation	18.96

  $\begin{array}{c}\text{Mean = }\frac{\sum x_i}{n}\\ =\frac{19195.19}{22}\\ =872.51\end{array}$

  $\begin{array}{c}\text{Standard Deviation = }\sqrt{\frac{\sum {\left(x_i-\overline{x}\right)}^2}{n}}\\ =\sqrt{\frac{7552.38}{22}}\\ =18.53\end{array}$

The mean and standard deviation for 2015 is 872.51 and 18.53.

To determine

To find the Population standard deviation for June.

Answer to Problem 41E

Standard Deviation = 164.65

Explanation of Solution

Calculation:

	June (Yi)	${\left(y_i-\overline{y}\right)}^2$
	871.22	111.94
	870.76	121.88
	868.31	181.98
	881.27	0.28
	873.32	71.91
	882.79	0.98
	889.42	58.06
	906.97	633.53
	908.53	714.49
	909.18	749.66
	903.87	487.08
	915.89	1162.13
	887.1	28.09
	877.53	18.23
	880.23	2.46
	871.48	106.50
	873.63	66.75
	857.23	603.68
	861.55	410.06
	845.72	1301.77
SUM	17636.00	6831.49
Mean	881.80
Standard Deviation	18.96

  $\begin{array}{c}\text{Mean = }\frac{\sum x_i}{n}\\ =\frac{17636}{20}\\ =881.8\end{array}$

  $\begin{array}{c}\text{Standard Deviation = }\sqrt{\frac{\sum {\left(x_i-\overline{x}\right)}^2}{n}}\\ =\sqrt{\frac{6831.49}{20}}\\ =18.48\end{array}$

The mean and standard deviation of sports model is 881.8 and 18.48.

To determine

To identify the month in which Google’s stock price are more volatile.

Answer to Problem 41E

May

Explanation of Solution

As the standard deviation in May is 18.53 and in June it is 18.48, it shows that May has higher standard deviation as compared to may, which shows that May is more volatile as compared to the June.