Question

3. A. The following are a list of 12 prices for Ford stock in 2018: 13.2, 10.6,10.8, 10.8, 11.4, 10, 9.3, 11.7, 11.05, 8.6, 9.4, 7.81. Describe this data using either a histogram or a boxplot. Be sure to show/explain how you obtain the numbers used in your graph.

B. The table below shows the prices of Ford stock on 3 different days. Calculate the mean and the standard deviation of the Ford stock prices.

Month	Ford	Toyota
Jan	13.20	150
July	11.05	130
Dec	7.81	110

3. The mean Toyota price $130 is and the standard deviation is $20. Calculate the correlation between the Ford and Toyota stock prices during this period.

What proportion of Staten Island residents have done Winter sessions?

Answer 1

3.

A.

Box plot for the given 12 prices for Ford stock:

Shown vertically:

13.25 13 12.75 12.5 12.25 12 11.75 11.5 11.25 10.75 10.5 10.25 10 9.75 9.5 9.25 8.75 8.5 8.25 7.75 Population size: 12 Median: 10.7 Minimum: 7.81 Maximum: 13.2 First quartile: 9.325 Third quartile: 11.3125 Interquartile Range: 1.9875 Outliers: none

Shown horizontally:

The data has no outliers and the distribution of the data is negatively skewed because the median, M is closer to the upper quartile, Q3. (For a distribution which is negatively skewed, the box plot will show the median closer to the upper quartile).

B.

Ford prices: 13.20, 11.05, 7.81. So, sample size, n= 3

Mean, $\bar{X}$ =$\Sigma X/n$ =(13.20+11.05+7.81)/3 =10.69

Standard deviation, s =$\sqrt{\Sigma(X-\bar{X})^2/(n-1)}$ =2.71

C.

Let X represent Ford prices and Y represent Toyota prices.

Std.deviation of Ford prices, Sx =2.71

Std.deviation of Toyota prices, Sy =20

X	Y	$X-\bar{X}$	$Y-\bar{Y}$	$(X-\bar{X}) (Y-\bar{Y})$​​
13.20	150	2.51	20	50.2
11.05	130	0.36	0	0
7.81	110	-2.88	-20	57.6
$\bar{X}$=10.69	$\bar{Y}$=130			$\Sigma [(X-\bar{X}) (Y-\bar{Y})] =$ 107.8

Covariance of X and Y =Cova(X,Y) =$\Sigma [(X-\bar{X}) (Y-\bar{Y})]/(n-1)$ =107.8/2 =53.9

Now, the correlation between Ford and Toyota prices is: r =Cova(X,Y)/(Sx. Sy) =53.9/[(2.71)(20)] =0.99, that is, almost 1. So, there is a perfect positive correlation between Ford and Toyota prices.