Chapter 10, Problem 1RE

NASDAQ 100 Stocks For Exercises 1-10, the data come from a random sample of 20 companies of the NASDAQ 100 taken on June 8, 2017. (Data from: www.morningstar.com.)

For Exercises 1 and 2, (a) write a frequency distribution; (b) draw a histogram.

The variable is the price of the stock (rounded to the nearest dollar).

123	35	76	38
45	62	50	111
180	108	65	46
66	100	64	144
57	107	48	110

To determine

Find the frequency table corresponding to the data came from a random sample of 20 companies of NASDAQ 100.

Explanation of Solution

Given:

Consider the data came from a random sample of 20 companies of NASDAQ 100

123	35	76	38
45	62	50	111
180	108	65	46
66	100	64	144
57	107	48	110

Calculation:

To draw the frequency table, sort the data set

35,38,45, 46,48,50,57,62,64,65,66,76,100,107,108,110,111,123,144,180

There is no repetition of data therefore the frequency of occurrence is 1 for all the data set hence the frequency distribution is

$x_i$	$f_i$	$x_i$	$f_i$
35	1	66	1
38	1	76	1
45	1	100	1
46	1	107	1
48	1	108	1
50	1	110	1
57	1	111	1
62	1	123	1
64	1	144	1
65	1	180	1

To determine

To graph: Draw the histogram corresponding to the corresponding to the data came from a random sample of 20 companies of NASDAQ 100.

Explanation of Solution

Given:

Consider the data came from a random sample of 20 companies of NASDAQ 100

123	35	76	38
45	62	50	111
180	108	65	46
66	100	64	144
57	107	48	110

Calculation:

To draw the frequency table sort the data set

35,38,45, 46,48,50,57,62,64,65,66,76,100,107,108,110,111,123,144,180

There is no repetition of data therefore the frequency of occurrence is 1 for all the data set hence the frequency distribution is

$x_i$	$f_i$	$x_i$	$f_i$
35	1	66	1
38	1	76	1
45	1	100	1
46	1	107	1
48	1	108	1
50	1	110	1
57	1	111	1
62	1	123	1
64	1	144	1
65	1	180	1

Range	Frequency
20-40	2
40-60	5
60-80	5
80-100	0
100-120	5
120-140	1
140-160	1
160-180	0
180-200	1

The y-axis represents frequency with a scale of $1\text{ unit of }y=1$ and the x-axis represents price with a scale of $1\text{ unit of }x=\$20$.

Hence, the histogram corresponding to the corresponding to the data came from a random sample of 20 companies of NASDAQ 100 is drawn.