Question

1. Consider the following data:

18, 20, 25, 31, 32, 38, 39, 40, 43, 49, 51, 54, 65, 74 Use 4 classes.

a. Class width :

b. Complete the following table.

????? ?????? ????? − ?????	Class Boundaries	Midpoint	Frequencies	Relative Frequencies	Cumulative Frequencies

c. Draw a histogram.

d. Draw a relative frequency histogram.

e. Make a stem-and-leaf display.

f. Find the interquartile range.

g. Make a box-and-whisker plot.

h. Determine the distribution shape. Please comment on all three plots.

i. Draw an ogive.

j. Find the mean.

k. Find the median.

l. Find the mode.

m. Find the variance.

n. Find the coefficient of variation.

2. Consider the following data:

x	13	11	8	6	5	3
y	2	5	7	6	4	2

a. ?̅ =

b. ?4 =

c. ? 7 =

d. ? 8 =

e. ? =

f. Make a scatter plot displaying the data.

g. Graph the least-squares line on your scatter plot.

h. What is the equation of the least-squares line.

i. What the value of the coefficient of determination ? : .

j. Interpret the coefficient of determination.

k. Predict y for x = 9.

3. A box contains 4 marbles, 1 red, 1 green, and 1 blue, 1 yellow. Describe the sample space of the following experiments.

a. Take 1 marble from the box, then replace it in the box and draw a second marble from the box.

b. Take 1 marble from the box, without replacing it, draw a second marble from the box.

4. A pair of fair dice are rolled. What is the probability that the second die lands on a higher value than does the first?

5. Two cards are chosen at random from a deck of 52 playing cards. What is the probability that they

a. both are aces

b. have the same value?

6. If a die is rolled 2 times, what is the probability that 5 comes at least once?

7. Urn A contains 3 red and 3 black balls, whereas urn B contains 4 red and 6 black balls. If a ball is randomly selected from each urn, what is the probability that the balls will be the same color?

8. Event A occurs with probability 0.2 and event B occurs with probability 0.5. Assume A and B are independent.

a. Find ?(? ??? ?)

b. Find ?(?|?)

c. Find ?(?|?).

9. A die with 8 sides is rolled. What is the probability of rolling a number less than 5?

10. Given the bivariate sample, (? E , ? E ), (? : , ? : ), … . . , (? H , ? H ) , suppose ? 7 =1, ? 8 = 6,

E ?̅ = 2, ?4 = 3, ? = . What is the equation of the least squares line.

J

10. A study conducted at a certain college shows that 75% of the school’s graduates find a job in their chosen field within a year after graduation. Find the probability that among 3 randomly selected graduates, at least one finds a job in their chosen field within a year of graduating.

Answer 1

1:

Following is the ordered data set:

S.No.	Data
1	18
2	20
3	25
4	31
5	32
6	38
7	39
8	40
9	43
10	49
11	51
12	54
13	65
14	74

We have:

Min = 18, Max = 74

Since we need 4 classes so class width should be

Class width =(Max-min) / 4 = (74-18) / 4 = 14

Let us assume class width 14+1=15. Following is the frequency distribution:

(c)

Following is the histogram:

(d)

Here we need to relative frequencies at y-axis. Following is the relative frequency histogram:

(e)

Following is the stem and leaf display:

(f)

There are 7 data values in the first half of data set. That is first quartile will be equal to 4th data value. So,

There are 7 data values in the second half of data set. That is third quartile will be equal to 11th data value. So,

The interquartile range will be

(g and k)

Median: There are 14 data values so median will be average of 7th and 8th data values That is

Following is the box and whisker plot:

(h)

Box plot shows that distribution is almost symmetric. It has no apparent outlier.

(i)

Following is the ogive:

(l)

Mode is the data value with highest frequency. Since all data values are unique so there is no mode of the data set.

(j, m and n):

Following table shows the calculations:

	X	(X-mean)^2
	18	545.5541204
	20	456.1257204
	25	267.5547204
	31	107.2695204
	32	87.55532041
	38	11.27012041
	39	5.55592041
	40	1.84172041
	43	2.69912041
	49	58.41392041
	51	92.98552041
	54	159.8429204
	65	558.9867204
	74	1065.55892
Total	579	3421.214286