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3 years ago

Each of 16 students measured the circumference of a tennis ball by four different methods, which were:

Business

1 answer:

antoniya [11.8K]3 years ago

7 0

Question Continuation

a. Compute the mean measurement for each method.

b. Compute the median measurement for. each method.

c. Compute the 20% trimmed mean measurement for each method.

Answer:

a. Mean

Mean A = 22.675

Mean B = 20.71875

Mean C = 21.0125

Mean D = 20.86875

b. Median

Median A = 23.45

Median B = 20.45

Median C = 21.0

Median D = 20.7

c. 20% Trimmed Mean

Trimmed Mean A = 23.14

Trimmed Mean B = 20.73

Trimmed Mean C = 21.04

Trimmed Mean D = 20.75

Explanation:

Mean = Σx/n

Where Σx= Summation of entries in each method

n = 16

Mean of Method A = (18.0 + 18.0 +18.0 + 19.0 + 22.0 + 22.0 + 22.5 + 22.9 + 24.0 + 24.0 + 25.0 +25.0 + 25.0 + 25.0 + 26.0 +26.4)/16

Mean A = 362.8/16

Mean A = 22.675

Mean of Method B = (18.8 + 18.9 + 18.9 + 19.8 + 20.1 + 20.4 + 20.4 + 20.4 + 20.6 + 20.5 + 21.2 + 21.9 + 22.0 + 22.0 + 22.0 + 23.6)16

Mean B = 331.5/16

Mean B = 20.71875

Mean of Method C = (20.2 + 20.5 + 20.5 + 20.7 + 20.8 + 20.9 + 21.0 + 21.0 + 21.0 + 21.0 + 21.0 + 21.5 + 21.5 + 21.5 + 21.5 + 21.6)/16

Mean C = 336.2/16

Mean C = 21.0125

Mean of Method D = (20.0 + 20.0 + 20.0 + 20.2 + 20.2 + 20.5 + 20.5 + 20.7 + 20.7 + 20.7 + 21.0 + 21.5 + 21.5 + 21.6 + 22.1 + 22.3)/16

Mean D = 333.9/16

Mean D = 20.86875

Median is the number(s) at the middle

Since the total number of points for each method is 16 and this is an even number we need to calculate the median as the average between the 8th and the 9th position of the data ordered from the smallest to the largest. If we do this we have that:

Method A

Arranged Data: 18.0, 18.0, 18.0, 19.0, 22.0, 22.0, 22.5, 22.9, 24.0, 24.0, 25.0, 25.0, 25.0, 25.0, 26.0, 26.4

The 8th and 9th data are: 22.9 and 24.0

Median = (22.9 + 24.0/2

Median = 46.9/2

Median A = 23.45

Method B

Arranged Data: 18.8, 18.9, 18.9, 19.8, 20.1, 20.4, 20.4, 20.4, 20.5, 20.6, 21.2, 21.9, 22.0, 22.0, 22.0, 23.6

The 8th and 9th data are: 20.4 and 20.5

Median = (20.4+20.5)/2

Median = 40.9/2

Median B = 20.45

Method C

Arranged Data: 20.2, 20.5, 20.5, 20.7, 20.8, 20.9, 21.0, 21.0, 21.0, 21.0, 21.0, 21.5, 21.5, 21.5, 21.5, 21.6

The 8th and 9th data are: 21.0 and 21.0

Median = (21.0 + 21.0)/2

Median = 42.0/2

Median C = 21.0

Method D

Arranged Data: 20.0, 20.0, 20.0, 20.2, 20.2, 20.5, 20.5, 20.7, 20.7, 20.7, 21.0, 21.5, 21.5, 21.6, 22.1, 22.3

The 8th and 9th data are: 20.7 and 20.7

Median = (20.7+20.7)/2

Median = 41.4/2

Median D = 20.7

The trimmed mean by 20% means that we'll calculate mean by removing the 20% from each of the tails.

20% of 16 = 3.2 (Approximated to 3)

So we need to remove 3 observations from both ends of the data.

Method A becomes

19.0, 22.0, 22.0, 22.5, 22.9, 24.0, 24.0, 25.0, 25.0, 25.0

Trimmed Mean A = (19.0+22.0+22.0+22.5+ 22.9+24.0+24.0+25.0+ 25.0+ 25.0)/10

Trimmed Mean A = 231.4/10

Trimmed Mean A = 23.14

Method B becomes

19.8, 20.1, 20.4, 20.4, 20.4, 20.6, 20.5, 21.2, 21.9, 22.0

Trimmed Mean B = (19.8+20.1+20.4+ 20.4+ 20.4+20.6+20.5+21.2+21.9+22.0)/10

Trimmed Mean B = 207.3/10

Trimmed Mean B = 20.73

Method C becomes

20.7, 20.8, 20.9, 21.0, 21.0, 21.0, 21.0, 21.0, 21.5, 21.5

Trimmed Mean C = (20.7+ 20.8+ 20.9+ 21.0+ 21.0+ 21.0+21.0+, 21.0+, 21.5+21.5)/10

Trimmed Mean C = 210.4/10

Trimmed Mean C = 21.04

Method D becomes

20.2, 20.2, 20.5, 20.5, 20.7, 20.7, 20.7, 21.0, 21.5, 21.5

Trimmed Mean D = (20.2+, 20.2+20.5+, 20.5+ 20.7+ 20.7+ 20.7 +, 21.0 +21.5 + 21.5)/10

Trimmed Mean D = 207.5/10

Trimmed Mean D = 20.75

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Further Explanation:

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A legally enforced agreement is considered a contract. An agreement is a promise between two parties to perform tasks for each other for some consideration. When an agreement becomes legally enforced, then it is considered as a contract. So the contract is a legally enforced promise between two parties for considerations. Both parties should get consideration and have a performance obligation.

Following factors are required for the contract:

Offer: A person should offer some consideration to another person for performing any activity or in the exchange of goods.

Acceptance of offer: The other person should accept the offer made by the first person.

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The contract between Pierre and Shayna:

In the current case, Pierre makes an offer to sell the painting to Shayna. Pierre leaves a message in the voicemail of Shayna, stating that if Shayna does not contact Pierre within one hour, then Pierre would consider that the Shayna wants to purchase the painting.

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Answer details:

Grade: Senior School

Subject: Business Law

Chapter: Contract Act

Keywords: Pierre, message, Shayna, voicemail, painting, mind, sell, steal, people, ASAP, hear, within an hour, not a valid contract, purchase a painting, lack of a(n), contract act, agreement, law, business law, promise, valid contract.

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3 years ago

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nikitadnepr [17]

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