Question

In: Statistics and Probability

2. The following data show the lengths of boats moored in a marina. The data are...

2. The following data show the lengths of boats moored in a marina. The data are ordered from smallest to largest.

16; 17; 19; 20; 20; 21; 22; 23; 24; 24; 24; 25; 25; 26; 26; 26; 27; 28; 29; 32; 33; 33; 34; 35; 37; 39; 40

a. Find the sample mean ?̅.

b. Find the mode.

c. Find the first quartile.

d. Find the median.

e. Find the third quartile.

f. Construct a box plot.

g. What percent of people surveyed visited a store at least 3 times?

h. Find the 40th percentile.

i. Construct a histogram of the data.

j. Find the percentile of data point 29.

k. State whether the data are symmetrical, skewed to the left, or skewed to the right.

l. Find the sample standard deviation.

Solutions

Expert Solution

a)

Mean = Sum of terms / Number of terms

= 725 / 27

= 26.8519

b)

The mode of a set of data is the value in the set that occurs most often.

Ordering the data from least to greatest, we get:

16   17   19   20   20   21   22   23   24   24   24   25   25   26   26   26   27   28   29   32   33   33   34   35   37   39   40   

Since both 24 and 26 occur 3 times, the modes are 24 and 26

c)

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

16   17   19   20   20   21   22   23   24   24   24   25   25   26   26   26   27   28   29   32   33   33   34   35   37   39   40   

So, the bottom half is

16   17   19   20   20   21   22   23   24   24   24   25   25   

The median of these numbers is 22.

first quartile = 22

d)

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

16   17   19   20   20   21   22   23   24   24   24   25   25   26   26   26   27   28   29   32   33   33   34   35   37   39   40   

So, the median is 26 .

e)

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

16   17   19   20   20   21   22   23   24   24   24   25   25   26   26   26   27   28   29   32   33   33   34   35   37   39   40   

So, the upper half is

26   26   27   28   29   32   33   33   34   35   37   39   40   

The median of these numbers is 33

third quartile = 33


Related Solutions

The following data show the lengths of boats moored in a marina. The data are ordered...
The following data show the lengths of boats moored in a marina. The data are ordered from smallest to largest. 16; 17; 19; 20; 20; 21; 22; 23; 24; 24; 24; 25; 25; 26; 26; 26; 27; 28; 29; 32; 33; 33; 34; 35; 37; 39; 40 g. What percent of people surveyed visited a store at least 3 times? h. Find the 40th percentile. i. Construct a histogram of the data. j. Find the percentile of data point 29....
The following data show the lengths of boats moored in a marina. The data are ordered...
The following data show the lengths of boats moored in a marina. The data are ordered from smallest to largest. 16; 17; 19; 20; 20; 21; 22; 23; 24; 24; 24; 25; 25; 26; 26; 26; 27; 28; 29; 32; 33; 33; 34; 35; 37; 39; 40 a. Find the sample mean ?̅. b. Find the mode. c. Find the first quartile. d. Find the median. e. Find the third quartile. f. Construct a box plot. g. What percent of...
Scott has operated a marina on Lake Huron for several years. The marina sells boats and...
Scott has operated a marina on Lake Huron for several years. The marina sells boats and provides a dock space and winter boat storage to its customers. On August 1, 2014 Craig purchased the marina from Scott. As part of the sale, Craig took over all the existing contracts Scott had for the storage and docking of boats. Nick had a contract with Scott to store his boat at the marina over the winter and to rent dock space as...
Use the following financial statements for Lake of Egypt Marina, Inc. LAKE OF EGYPT MARINA, INC...
Use the following financial statements for Lake of Egypt Marina, Inc. LAKE OF EGYPT MARINA, INC Balance Sheet as of December 31, 2015 and 2014 (in millions of dollars) 2015 2014 2015 2014   Assets   Liabilities and Equity   Current assets:   Current liabilities:      Cash and marketable securities $ 100 $ 48      Accrued wages and taxes $ 60 $ 48      Accounts receivable 110 72      Accounts payable 110 72      Inventory 301 174      Notes payable 70 60         Total $ 511 $ 294         Total $ 240...
Use the following financial statements for Lake of Egypt Marina, Inc. LAKE OF EGYPT MARINA, INC...
Use the following financial statements for Lake of Egypt Marina, Inc. LAKE OF EGYPT MARINA, INC Balance Sheet as of December 31, 2015 and 2014 (in millions of dollars) 2015 2014 2015 2014   Assets   Liabilities and Equity   Current assets:   Current liabilities:      Cash and marketable securities $ 80 $ 42      Accrued wages and taxes $ 40 $ 30      Accounts receivable 120 66      Accounts payable 90 60      Inventory 222 168      Notes payable 50 54         Total $ 422 $ 276         Total $ 180...
Use the following financial statements for Lake of Egypt Marina, Inc. LAKE OF EGYPT MARINA, INC...
Use the following financial statements for Lake of Egypt Marina, Inc. LAKE OF EGYPT MARINA, INC Balance Sheet as of December 31, 2015 and 2014 (in millions of dollars) 2015 2014 2015 2014 Assets Liabilities and Equity Current assets: Current liabilities: Cash and marketable securities $ 50 $ 56 Accrued wages and taxes $ 50 $ 48 Accounts receivable 60 52 Accounts payable 55 44 Inventory 205 96 Notes payable 60 40 Total $ 315 $ 204 Total $ 165...
Use the following financial statements for Lake of Egypt Marina, Inc. LAKE OF EGYPT MARINA, INC...
Use the following financial statements for Lake of Egypt Marina, Inc. LAKE OF EGYPT MARINA, INC Balance Sheet as of December 31, 2015 and 2014 (in millions of dollars) 2015 2014 2015 2014   Assets   Liabilities and Equity   Current assets:   Current liabilities:      Cash and marketable securities $ 80 $ 42      Accrued wages and taxes $ 40 $ 30      Accounts receivable 120 66      Accounts payable 90 60      Inventory 222 168      Notes payable 50 54         Total $ 422 $ 276         Total $ 180...
Use the following financial statements for Lake of Egypt Marina, Inc. LAKE OF EGYPT MARINA, INC...
Use the following financial statements for Lake of Egypt Marina, Inc. LAKE OF EGYPT MARINA, INC Balance Sheet as of December 31, 2015 and 2014 (in millions of dollars) 2015 2014 2015 2014 Assets Liabilities and Equity Current assets: Current liabilities: Cash and marketable securities $ 72 $ 48 Accrued wages and taxes $ 56 $ 54 Accounts receivable 80 60 Accounts payable 80 66 Inventory 294 186 Notes payable 48 54 Total $ 446 $ 294 Total $ 184...
Use the following financial statements for Lake of Egypt Marina, Inc. LAKE OF EGYPT MARINA, INC...
Use the following financial statements for Lake of Egypt Marina, Inc. LAKE OF EGYPT MARINA, INC Balance Sheet as of December 31, 2015 and 2014 (in millions of dollars) 2015 2014 2015 2014 Assets Liabilities and Equity Current assets: Current liabilities: Cash and marketable securities $ 40 $ 30 Accrued wages and taxes $ 32 $ 24 Accounts receivable 32 39 Accounts payable 40 27 Inventory 175 60 Notes payable 32 30 Total $ 247 $ 129 Total $ 104...
Use the following financial statements for Lake of Egypt Marina, Inc. LAKE OF EGYPT MARINA, INC....
Use the following financial statements for Lake of Egypt Marina, Inc. LAKE OF EGYPT MARINA, INC. Balance Sheet as of December 31, 2021 and 2020 (in millions of dollars) 2021 2020 2021 2020 Assets Liabilities and Equity Current assets: Current liabilities: Cash and marketable securities $ 75 $ 65 Accrued wages and taxes $ 40 $ 43 Accounts receivable 115 110 Accounts payable 90 80 Inventory 200 190 Notes payable 80 70 Total $ 390 $ 365 Total $ 210...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT