STAT 118 - CHAPTER 3 - HW & EXCEL

According to Chebyshev's theorem, at least what percent of any set of observations will be within 1.8 standard deviations of the mean? (Round your answer to the nearest whole percent.)

1 - ( 1 / (1.8^2)) = .6913580247 .6913580247 x 100 = 69%

Suppose you go to the grocery store and spend $61.09 for the purchase of 13 items. What is the mean price per item? (Round your answer to 2 decimal places.)

$61.09 / 13 = 4.70

In June, an investor purchased 225 shares of Oracle (an information technology company) stock at $19 per share. In August, she purchased an additional 260 shares at $27 per share. In November, she purchased an additional 470 shares at $29. What is the weighted mean price per share? (Round your answer to 2 decimal places.)

(225 x $19) + (260 x $27) + (470 x $29) = 24,925 225 + 260 + 470 = 955 24,925 / 955 = $26.10 per share

In 1998, a total of 40,247,000 taxpayers in the United States filed their individual tax returns electronically. By the year 2013, the number increased to 153,377,544. What is the geometric mean annual increase for the period? (Round your answer to 2 decimal places.)

2013 - 1998 = 15 years 153,377,544 / 40,247,000 = 3.810906254 (3.810906254 ^ (1/15 years)) = 1.093289602 1.093289602 - 1 = .0932896021 .0932896021 x 100 = 9.33%

The information below shows the cost for a year of college at a public and at a private college in 2003-04 and 2014-15. For the period of time between 2003-04 and 2014-15, what is the annual rate of change in the cost to attend each type of college? Type of College 2003-04 2014-15 Public (four-year) $3,120 $7,630 Private (four-year) $5,536 $13,800 b. Compare the rates of increase.The rate of increase is (Click to select) for private colleges.

2014 - 2003 = 11 Public [ ( $7,630 / $3,120 ) ^ (1/11) ] - 1 = .0846918038 x 100 = 8.47% Private [ ($13,800 / $5,536) ^(1/11) ] - 1 = .0865809617 x 100 = 8.66% b. higher

Compute the mean of the following population values: 2, 3, 5, 7, 6.

4.6

Compute the mean of the following population values: 4, 3, 5, 7, 6.

5 (4 + 3 + 5 + 7 + 6) / 5

The Bookstall Inc. is a specialty bookstore concentrating on used books sold via the Internet. Paperbacks are $1.55 each, and hardcover books are $3.90. Of the 90 books sold last Tuesday morning, 80 were paperback and the rest were hardcover.What was the weighted mean price of a book?

80 Paperbacks for $1.55 each 10 Hardcover for $3.90 each (90 total books - 80 paperbacks) = 10 were hardcover (80 x $1.55) + (10 x $3.90) = $163 $163 / 90 books = $1.81

The Consumer Price Index is reported monthly by the U.S. Bureau of Labor Statistics. It reports the change in prices for a market basket of goods from one period to another. The index for 1998 was 166.5. By 2015, it increased to 286.6. What was the geometric mean annual increase for the period? (Round your answer to 2 decimal places.)

Geometric Mean = [ (Value2 / Value1) ^ (1 / (2015-1998) ) ] - 1 2015-1998 = 17 years Steps: 1) 286.6 / 166.5 = 1.721321321 2) 1.721321321 ^ (1/17) = 1.032462371 3) 1.032462371 - 1 = .0324623707 4) .0324623707 x 100 = 3.25%

The Split-A-Rail Fence Company sells three types of fence to homeowners in suburban Seattle, Washington. Grade A costs $5.00 per running foot to install, Grade B costs $6.50 per running foot, and Grade C, the premium quality, costs $8.00 per running foot. Yesterday, Split-A-Rail installed 270 feet of Grade A, 300 feet of Grade B, and 100 feet of Grade C. What was the mean cost per foot of fence installed? (Round your answer to 2 decimal places.)

Grade A: $5.00 and 270 feet Grade B: $6.50 and 300 feet Grade C: $8.00 and 100 feet Total feet: 270 + 300 + 100 =670 feet (270 x $5) + (300 x $6.5) + (100 x $8) = $4,100 $4,100 / 670 feet = $6.12

The following frequency distribution reports the electricity cost for a sample of 50 two-bedroom apartments in Albuquerque, New Mexico, during the month of May last year. Electricity CostFrequency $ 80 up to 100 3 100 up to 120 8 120 up to 140 12 140 up to 160 16 160 up to 180 7 180 up to 200 4 Total 50 a. Estimate the mean cost. b. Estimate the standard deviation.

MIDPOINT: (80 + 10) / 2 = 90 (100 + 120) / 2 = 110 (120 + 140) / 2 = 130 (140 + 160) / 2 = 150 (160 + 180) / 2 = 170 (180 + 200) / 2 = 190 a. MEAN: [ 3(90) + 8(110) + 12(130) + 16(150) + 7(170) + 4(190) ] / 50 = 141.2 b. Standard Deviation: Variance = [ 3(90-141.2)^2 + 8(110-141.2)^2 + 12(130-141.2)^2 + 16(150-141.2)^2 + 7(170-141.2)^2 + 4(190-141.2)^2 ] / 49 =688.33 Standard deviation = squareroot(688.3) = 26.24 c. Lower: Mean - 2(Stdev) Upper: Mean + 2(Stdev) Lower: 141.2 - 2(26.24) = 88.72 Upper: 141.2 + 2(26.24) = 193.68

Sally Reynolds sells real estate along the coastal area of Northern California. Below are her total annual commissions between 2008 and 2018. Find the mean, median, and mode of the commissions she earned for the 11 years. (Round your answers to 2 decimal places.)

Mean: 231.36 Median: 233.30 Mode: 248.14 Formulas to use in Excel Mean: =Average() Median: =Median Mode: =Mode()

The IRS was interested in the number of individual tax forms prepared by small accounting firms. The IRS randomly sampled 42 public accounting firms with 10 or fewer employees in the Dallas-Fort Worth area. The following frequency table reports the results of the study. Number of Clients Frequency 16 up to 22 5 22 up to 28 8 28 up to 34 12 34 up to 40 14 40 up to 46 3 Estimate the mean and the standard deviation. (Round squared deviations to nearest whole number and final answers to 2 decimal places.)

Mean: 31.29 St. Deviation: 6.88 To find the Mean Midpoint (M): (16+22)/2 = 19 (22+28)/2 = 25 (28+34)/2 = 31 (34+40)/2 = 37 (40+46)/2 = 43 MEAN (x): [ 5(19) + 8(25) + 12(31) + 14(37) + 3(43) ] / 42 = 31.29 Standard Deviation:

Advertising expenses are a significant component of the cost of goods sold. Listed below is a frequency distribution showing the advertising expenditures for 60 manufacturing companies located in the Southwest. Estimate the mean and the standard deviation of advertising expenses. (Round squared deviations to nearest whole number and final answers to 2 decimal places.) Advertising Expenditure($ millions) Number of Companies (frequencies) 25 up to 35 5 35 up to 45 10 45 up to 55 21 55 up to 65 16 65 up to 75 8 Total 60

Mean: 52 St. Dev: 11.32 To find the Mean Midpoint (M): (25+35)/2 = 30 (35+45)/2 = 40 (45+55)/2 = 50 (55+65)/2 = 60 (65+75)/2 = 70 MEAN (x): [ 5(30) + 10(40) + 21(50) + 16(60) + 8(70) ] = 3,120 3,120 / 60 = 52 To find Standard Deviation: Step 1: Midpoint (M) - Mean (x) 30 - 52 = -22 40 - 52 = -12 50 - 52 = - 2 60 - 52 = 8 70 - 52 = 18 Step 2: (M - x)^2 (-22)^2 = 484 (-12)^2 = 144 (-2)^2 = 4 (8)^2 = 64 (18)^2 = 324 Step 3: Frequency*[(M-x)^2] 5 * 484 = 2,420 10 * 144 = 1,440 21 * 4= 84 16 * 64 = 1,024 8 * 324 = 2,592 Total : 7,560 n= 60 manufacturing companies Square root of [ 7,560 / (60-1) ] = 11.32

Estimate the mean and the standard deviation of the following frequency distribution showing the ages of the first 60 people in line on Black Friday at a retail store. Class Frequency 20 up to 30 7 30 up to 40 12 40 up to 50 21 50 up to 60 18 60 up to 70 12

Midpoint (20 + 30) / 2 = 25 (30 + 40) / 2 = 35 (40 + 50) / 2 = 45 (50 + 60) / 2 = 55 (60 + 70) / 2 = 65 Mean: [ 7(25) + 12(35) + 21(45) + 18(55) + 12(65) ] / 70 = 47.29

The distribution of the weights of a sample of 1,350 cargo containers is symmetric and bellshaped. Required: a. According to the Empirical Rule, what percent of the weights will lie between X−1s and X⁢+1s ? (Round your answer to 1 decimal place.) b. According to the Empirical Rule, what percent of the weights will lie between X and X + 1s ? (Round your answer to 2 decimal places.) c. Above X + 1s ? (Round your answer to 2 decimal places.)

The empirical rule can be broken down into three parts: 68% of data falls within the first standard deviation from the mean. 95% fall within two standard deviations. 99.7% fall within three standard deviations a. 68% 34% + 34% b. 34% c. 16% 13.5% + 2.35% + .15%

The Loris Healthcare System employs 200 persons on the nursing staff. Fifty are nurse's aides, 50 are practical nurses, and 100 are registered nurses. Nurse's aides receive $12 an hour, practical nurses $20 an hour, and registered nurses $29 an hour.What is the weighted mean hourly wage? (Round your answer to 2 decimal places.)

Total 200 persons 50 Nurse's aides = $12 an hour 50 Practical Nurses = $20 an hour 100 Registered Nurses = $29 an hour (50 x $12) + (50 x $20) + (100 x $29) = $4,500 $4,500 / 200 persons = $22.5 per hour

A sample of 25 undergraduates reported the following dollar amounts of entertainment expenses last year: 697 755 689 738 720 736 710 745 747 765 685 749 720 775 713 703 692 756 773 768 765 695 739 687 709 a. Find the mean, median, and mode of this information. (Round the "Mean" to 2 decimal places.) b. What are the range and standard deviation? c. Use the Empirical Rule to establish an interval that includes about 95% of the observations. (Round your answers to 2 decimal places.)

USING CALCULATOR: To find MEAN and MEDIAN and STANDARD DEVIATION and RANGE Mean x̅ Median: Med Standard Deviation: Sx Range: maxX - minX Method 1: Enter DATA into LISt Press STAT. Arrow to the right to CALC. Now choose option #1: 1-Var Stats. When 1-Var Stats appears on the home screen, tell the calculator the name of the list you are using (such as: 1-Var Stats L1)Press ENTER. Arrow up and down the screen to see the statistical information about the data. Method 2: Press 2nd MODE (QUIT) to return to the home screen. Press 2nd STAT (LIST). Arrow to the right to MATH. Choose option #3: mean(2nd 1 (l1)) #4: median(2nd 1 (L1)) #7: stdDev(2nd 1 (L1)) #8: variance(2nd 1 (L1)) To find MODE (While there is no specific calculator function to find the mode, the calculator is helpful in ordering the data so that you can find the mode easily.) Sort the data into ascending or descending order to help find the mode. STAT, #2 SortA(, and specify L1, or the list you are using. Look at the list (STAT, #1 EDIT). a. MEAN: x̅: 729.24 MEDIAN: 736 MODE: 720 and 765 b. RANGE: 775 - 685 = 90 STANDARD DEVIATION: 29.92 c. Emperical rule for 95% observations is: Mean - 2(Stdev) and Mean + 2(Stdev) Lower value = 729.24 - 2(29.92) = 669.40 Upper value = 729.24 + 2(29.92) = 789.08 95% of the observations lie between $669.40 and $789.08

Refer to the Lincolnville School District bus data. Prepare a report on the maintenance cost for last month. Be sure to answer the following questions in your report. Required: a-1. Around what values do the data tend to cluster? a-2. Specifically what was the mean maintenance cost last month? What is the median cost? (Round your answers to 2 decimal places.) a-3. Is one measure more representative of the typical cost than the others? b-1. What is the range of maintenance costs? What is the standard deviation? b-2. About 95% of the maintenance costs are between what two values?

Use attached EXCEL DATA on FILE Mean: =Average(F2:F81) Median: =Median(F2:F81) Max (Largest Value): =Max(F2:F81) Min (Smallest Value): =Max(F2:F81) Standard Deviation: =STDEV(F2:F81) a-1. a-2. Mean: $4,551.89 Median: $4,178.50 a-3. NO b-1 STANDARD DEVIATION: $2,331.53 RANGE: 10,070 Max: 10,575 Min: 505 b-2 About 95% from the Empirical Rule is X + 2s (Upper) and X - 2s (Lower Mean +/- 2(*Standard Deviation) Upper: $4,551.89 - 2($2,331.53) = Lower: $4,551.89 + 2($2,331.53) =

The table below shows the percent of the labor force that is unemployed and the size of the labor force for three counties in northwest Ohio. Jon Elsas is the Regional Director of Economic Development. He must present a report to several companies that are considering locating in northwest Ohio. What would be an appropriate unemployment rate to show for the entire region?

Wood: 4.5% unemployed and 15,300 size of the workforce Ottawa: 3.0% unemployed 10,400 size of the workforce Lucas: 10.2% unemployed and 150,600 size of the workforce Total size of the workforce: 15,300 + 10,400 + 150,600 = 176,300 (15,300 x 0.045) + (10,400 x 0.03) + (150,600 x 0.102) = 16,361.7 (16,361.7 / 176,300) x 100 = 9.28%

In 2012 there were 233.3 million cell phone subscribers in the United States. By 2019 the number of subscribers increased to 268.1 million. Required: a. What is the geometric mean annual percent increase for the period? Further, the number of subscribers is forecast to increase to 277.8 million by 2023. What is the rate of increase from 2019 to 2023? (Round your answers to 2 decimal places.) b. Is the rate of increase expected to slow?

a) 2012 to 2019 2019 - 2012 = 7 yrs [ (268.1 / 233.3) ^ (1/7) ] - 1 = .0200606882 x 100 = 2.01% 2019 to 2023 2023 - 2019 = 4 years [ (277.8 / 268.1) ^ (1/4) ] - 1 = .89% b) Yes

The manager of the local Walmart Supercenter is studying the number of items purchased by customers in the evening hours. Listed below is the number of items for a sample of 30 customers. 15 8 6 9 9 4 18 10 10 12 12 4 7 8 12 10 10 11 9 13 5 6 11 14 5 6 6 5 13 5 a. Find the mean and the median of the number of items. (Round "Mean" to 1 decimal place.) b. Find the range and the standard deviation of the number of items. (Round "Standard deviation" to 3 decimal places.) c. Organize the number of items into a frequency distribution. d. Find the mean and the standard deviation of the data organized into a frequency distribution.

a. MEAN: 9.1 MEDIAN: 9 b. RANGE: 14 St.Dev: 3.566 d. Mean: 9 St.Dev: 3.553

The annual report of Dennis Industries cited these primary earnings per common share for the past 5 years: $2.54, $1.15, $2.14, $4.28, and $9.48. Assume these are population values. Required: a. What is the arithmetic mean primary earnings per share of common stock? (Round your answer to 2 decimal places.) b. What is the variance? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

a. Arithmetic Mean = 4.2 ($2.54 + $1.15 + $2.14 + $4.28 + $9.48) / 5 = $3.92 b. Variance: 5.76 use graphing calculator: Steps: STAT -> 1:Edit... -> input values -> right arrow to CALC -> 1:1-Var Stats -> ENTER x̅ = $3.92 σx = 2.959353984 To find Population Variance σ^2 2.959353984 ^ 2 = 5.76 with graphing calculator: VARS -> 5:Statistics... -> 4:σx -> x^2 -> ENTER σx^2 = 8.76 hint: VARIANCE is the SQUARED of the STANDARD DEVIATION

Consider these five values a population: 6, 3, 6, 0, and 6. a. Determine the mean of the population. (Round your answer to 1 decimal place.) b. Determine the variance. (Round your answer to 2 decimal places.)

a. Arithmetic Mean = 4.2 (6 + 3 + 6 + 0 + 6) / 5 = 4.2 b. Variance: 5.76 use graphing calculator: Steps: STAT -> 1:Edit... -> input values -> right arrow to CALC -> 1:1-Var Stats -> ENTER x̅ = 4.2 σx = 2.4 To find Population Variance σ^2 2.4 ^ 2 = 5.76 with graphing calculator: VARS -> 5:Statistics... -> 4:σx -> x^2 -> ENTER σx^2 = 5.76

The unemployment rate in the state of Alaska by month is given in the table below: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 8.8 7.3 8.5 8.3 6.7 6.0 6.1 8.9 7.4 7.2 7.3 8.4 a. What is the arithmetic mean of the Alaska unemployment rates? b. Find the median and the mode for the unemployment rates. c-1. Compute the arithmetic mean and median for just the winter (Dec-Mar) months. c-2. Is it much different?

a. Arithmetic Mean: 7.58 =Average(B2:B13) b. Median: 7.35 =Median(B2:B13) Mode: 7.30 =Mode(B2:B13) (Dec-Mar) c-1. Mean: 8.25 =Average(B13,B2:B4) Median: 8:45 =Median(B13,B2:B4) Unemployment Rates Ordered from Low to High (Dec-Mar) 7.3 8.4 8.5 8.8 (8.4+8.5)/2 = 8.45 c-2: The winter unemployment rates are higher.

The accounting firm of Crawford and Associates has five senior partners. Yesterday the senior partners saw three, six, three, three, and five clients, respectively. Required: a. Compute the mean and median number of clients seen by the partners. (Round your answers to 1 decimal place.) b. Is the mean a sample mean or a population mean?

a. Mean: 4 ( 3 + 6 + 3 + 3 + 5) / 5 = Median: 3 Number of clients in ORDER: 3 , 3, 3, 5 , 6 b. population mean because the clients from all of the partners were included.

The personnel files of all eight employees at the Pawnee location of Acme Carpet Cleaners Inc. revealed that during the last 6-month period they lost the following number of days due to illness: 10 1 3 2 4 0 0 2 All eight employees during the same period at the Chickpee location of Acme Carpets revealed they lost the following number of days due to illness: 1 1 2 4 5 7 5 5 a. Calculate the range and mean for the Pawnee location and the Chickpee location. b-1. Based on the data which location has fewer lost days? b-2. Based on the data which location has less variation?

n = 8 employees a. Pawnee (from lowest to highest) 0 + 0 + 1 + 2 + 2 + 3 + 4 + 10 = 22 days Mean: 22 / 8 employees = 2.75 Range: Max - Min Max: 10 Min: 0 Range: 10 - 0 = 10 Chickpee (lowest to highest) 1 + 1 + 2 + 4 + 5 + 5 + 5 + 7 = 30 days Mean: 30 / 8 = 3.75 Range: 7 - 1 = 6 b-1: Pawnee location Pawnee has a total of 22 lost days Chickpee has a total of 30 lost days b-2. Chickpee location

The ages of a sample of Canadian tourists flying from Toronto to Hong Kong were 22, 24, 63, 45, 50, 19, 57, 54, 41, and 41. (Round the range to nearest whole number and the standard deviation to 2 decimal places.) Required: a. Compute the range. b. Compute the standard deviation.

n=10 Sample in ORDER: 19, 22, 24, 41, 41, 45, 50, 54, 57, 63 RANGE: Largest Value - Smallest Value a. RANGE: 63 - 19 = 44 b. Sx= 15.41 Use graphing calculator: Press STAT. Arrow to the right to CALC. Now choose option #1: 1-Var Stats. When 1-Var Stats appears on the home screen, tell the calculator the name of the list you are using (such as: 1-Var Stats L1)Press ENTER. Sx is the standard devation

When we compute the mean of a frequency distribution, why do we refer to this as an estimated mean? Because the exact values in a frequency distribution are ____________, the _____________ of the class is used for every member of that class.

not known midpoint

The first Super Bowl was played in 1967. The cost for a 30-second commercial was $42,000. The cost of a 30-second commercial for Super Bowl 42 was played on February 4, 2008, in Minneapolis, Minnesota, was $2.7 million. What was the geometric mean rate of increase for the 42-year period? (Round your answer to 2 decimal places.)

steps: ( $2,700,000 / $42,000) ^ (1/42) = 1.104206615 1.104206615 - 1 = 0.1042066152 0.1042066152 x 100 = 10.42%