**Week 3 Problems**

**1. An industrial group reports that there were approximately 122,000 industrial robots operating in a region last year. The graph shows the percentages of industrial robot units assigned to each of six task categories. **

Complete parts a through e bellow.

**a. What type of graph is used to describe the data?**

**A. Pie chart**

B. Bar graph

C. Pareto diagram

**b. Identify the variable measured for each of the 122,000 industrial robots**

A. Percentage of industrial robots

B. Number of industrial robots

C. Efficiency of each industrial robot

**D. Task of each industrial robot**

**c. Use the graph to identify the task that uses the lowest percentage of industrial robots**

A. Arc welding

B. Assembly

C. Material handling

**D. Material removal**

E. Dispensing/coating

F. Spot welding

d. How many of the 122,000 industrial robots are used for assembly?

**6100** industrial robots

e. What percentage of industrial robots are used for either arc welding or dispensing/coating?

**43%**

2. In one university, language professors incorporated a 10-week extensive readings program to improve students’ Japanese reading comprehension. The professor collected 262 books originally written for Japanese children and required their students to read at least 40 of them as part of the grade in course. The books were categorized into reading levels (color-coded for easy selection) according to length and complexity. Complete parts a trough c.

a. Compute the relative frequencies in each category.

Reading Level Relative frequency

Level 1 (Red) .160

Level 2 (Blue) .279

Level 3 (Yellow) .195

Level 4 (Pink) .317

Level 5 (Orange) .038

Level 6 (Green) .011

b. Construct a relative frequency bar graph for the data. Choose the correct graph bellow

A. **B.** ** C. **

**Correct answer B**

c. Convert the relative frequency bar graph into a Pareto diagram. Interpret the graph. Choose the correct graph bellow

**A. **** B. C. **

**Correct answer A**

Use the diagram to identify the reading level that occurs more often. Choose the correct answer bellow

**Level 4** Level 3

Level 2 Level 6

Level 1 Level 5

**3. One organization estimates that there are 13,140 rhinoceroses living in the wild in a continent. A breakdown of the number of rhinos of each species is reported in the accompanying table. Complete parts a trough c.**

a. One of the 13,140 rhinoceroses is selected and the species of the rhinoceros is determined. What type of data (quantitative or qualitative) is measured?

**A. Qualitative**

B. Quantitative

b. Construct a frequency bar chart for the data. Choose the correct graph bellow.

A. B. C. **D.**

**Correct answer D**

c. Convert the frequency bar chart, part b, into a Pareto diagram. Interpret the results

A. B. C. D.

**Correct answer D**

The most populated species of rhinoceros appear to be the **African White** and the least most populated species seems to be the **Javan**

**4. One organization estimates that there are 13,090 rhinoceroses living in the wild in a continent. A breakdown of the number of rhinos of each species is reported in the accompanying table. Complete parts a through c.**

a. One of the 13,090 rhinoceroses is selected and the species of the rhinoceroses is determined. What type of data (qualitative or quantitative) is measured?

A. Quantitative

**B. Qualitative**

b. construct a frequency bar chart for the data. Choose the correct graph bellow.

A. **B.** C. D.

**Correct answer B**

c. Convert the frequency bar chart, part b, into a Pareto diagram. Interpret the results. Choose the correct graph bellow.

A. **B.** C. D.

**Correct answer B**

Interpret the results

The most populated species of rhinoceros appear to be **African White** and the least most populated species seems to be the **Javan**

5. A government study found that the number of non-cash payments in a country reached 92.7 billion transactions during the year 2007. The pie chart to the right describes the proportions of these non-cash transactions that were made with credit cards (CC), debit cards (D), checks (C), electronic benefit transfers (EBT) cards, and automatic clearing house (ACH) payments. Complete parts a trough d.

a. Describe the population of interest in the study. Choose the correct answer bellow.

A. The population is the country making the transactions during the year

B. The population is the government that conducted the survey

C. The population is all transactions made using a credit card or debit card during the year

**D. The population is all non-cash transactions made during the year**

b. Estimate the number of non-cash payments in 2007 that were made with credit cards

**21.32 billion**

c. What percentage of all non-cash payments in 2007 were made with either credit or debit cards?

**49%**

d. Convert the pie chart into a Pareto diagram and interpret the figure. Choose the correct graph bellow

A. B. **C. **

**Correct answer C**

Interpret the figure. Choose the correct answer bellow.

A. The figure shows that EBT cards, ACH payments, and credit cards have approximately the same percentage and that checks have almost no representation.

B. The figure shows that the data are different when viewed in a pie chart than in a Pareto diagram

**C. The figure shows that checks, debit cards, and credit cards have the largest percentages and that EBT cards have almost no representation**

D. An interpretation cannot be made given the information of this problem

6. A group of marketing professors asked every fourth adult entrant to a mall to participate in a study. A total of 106 shoppers agreed to answer the question, “Made locally’ means what percentage of local labor and materials?” The responses of the 106 shoppers are summarized in the table to the right. Complete parts a trough c bellow.

a. What type of data-collection method was used?

A. Designed experiment

**B. Survey**

C. Observational study

D. Published source

b. What type of variable, quantitative or qualitative, is measured?

A. Qualitative

**B. Quantitative**

c. Present the data in the table in graphical form. Which bar graph bellow correctly represents the data in the table?

A. B.

**Correct answer A**

**7. Use the relative frequency table shown to the right to calculate the number of the 400 measurements**** falling into each of the measurement classes. Then graph a frequency histogram for these data.**

Calculate the number of measurements that fall into each class

Choose the correct graph bellow

A. B.

C.

**Correct answer C**

**8. Use the relative frequency table shown to the right to calculate the number of the 400 measurements falling into each of the measurement classes. Then graph a frequency histogram for these data.**

Calculate the number of measurements that fall into each class

Choose the correct graph bellow

**A.**** **** B. **

C.

**Correct answer A**

**9. Consider the stem-and-leaf display to the right: **

**a. How many observations were in the original data set?**

**b. In the bottom row of the stem-and-leaf display, identify the stem, and the numbers in the original data set represented by this stem and its leaves.**

**c. Re-create all the numbers in the data set and construct a dot plot**

a. How many observations were in the original data set?

There were **14** observations in the original data set

b. In the bottom row of the stem-and-leaf display, identify the stem, and the numbers in the original data set represented by this stem and its leaves.

A. The stem is 078 and the leaf is 0. The number in the original data set is 10

B. The stem is 0 and the leaves are 0, 7, 8. The numbers in the original data set are 10, 17, 18

**C. The stem is 0 and the leaves are 0, 7, 8. The numbers in the original data set are 0, 7, 8.**

D. The stem is 078 and the leaf is 0. The number in the original data set is 0

c. Re-create all the numbers in the data set and construct a dot plot

A. B.

C.

**10. Certain measurements are summarized in the histogram to the right. What percentage of the measurement are greater then 12?**

The histogram shows that **35%** of the measurements are greater than 12

**11. Calculate the mean and median of the following grade point averages.**

**2.1 3.8 2.7 3.4 2.3 3.3**

Mean=**2.93**

Median=**3**

**12. Calculate the mean for samples for which the sample size and ∑x are given bellow**

**a. n=10, ∑x=83**

**b. n=16, ∑x=352**

**c. n=45, ∑x=36**

**d. n=18, ∑x=238**

_

a. X = 8.3

_

b. X = 22

_

c. x = .8

_

d. x = 13.22

**13. Five banks have been ranked by the amount charged to credit and debit cards issued by the banks. The table to the right gives the total amount charged in 2007 for the top ranked banks.**

**a. Find the mean amount charged for the top five banks and practically interpret this value**

**b. Find the median amount charged for the top five banks and practically interpret this value.**

a. The mean amount charged for the top five banks is **$359.9** billion

Interpret this value. Choose the correct answer bellow

A. This value is the amount that was charged most often by the top 5 banks.

**B. This value is the average amount charged by the top 5 banks**

C. Approximately half of the 5 charged amounts are greater than this value

b. The median amount charged for the top five banks is $450.57 billion

Interpret this value. Choose the correct answer bellow

**A. Approximately half of the 5 charged amounts are greater than this value**

B. This value is the amount that was charged most often by the top 5 banks

C. This value is the average amount charged by the top 5 banks

**14. Calculate the range, variance, and standard deviation for the following sample**

**5, 2,1,0,1**

Range=5

Sample variance s²=3.7

Sample standard deviation, s=1.92

**15. Calculate the variance and standard deviation for samples with the following statistics**

**a. n=12, ∑x****²****=83, ∑x=24**

**b. n=37, ****∑x****²****=371, ∑x=90**

**c. n=19, ∑x****²****=19, ∑x=18**

a. The variance is 3.182

The standard deviation is 1.784

b. The variance is 4.224

The standard deviation is 1.784

c. The variance is .108

The standard deviation is .329

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