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natta225 [31]
3 years ago
5

Suppose the following data set represents the starting salaries for the population of teachers from seven states: $41,027, $35,9

01, $31,159, $33,664, $35,166,$39,338, $32,691
A) calculate the mean of the data set
B) calculate the 5 number summary
C) calculate the standard deviation of this data set
Mathematics
1 answer:
aalyn [17]3 years ago
6 0

Answer:

See explanation

Step-by-step explanation:

Arrange the salaries $41,027, $35,901, $31,159, $33,664, $35,166, $39,338, $32,691 in ascending order:

$31,159, $32,691, $33,664, $35,166, $35,901, $39,338, $41,027

A) The mean salary (to the nearest dollar) is

\dfrac{\$31,159+\$32,691+\$33,664+\$35,166+\$35,901+\$39,338+\$41,027}{7}=\$35,564

B) Minimum = \$31,159

Q_1=\$32,691

Median =\$35,166

Q_2=\$39,338

Maximum =\$41,027

C) The standard deviation of this data set can be calculated using formula

\sigma=\sqrt{\dfrac{\sum(x_i-\text{mean})^2}{n}}

First, find (x_i-\text{mean})^2:

(31,159-35,564)^2=19,404,025\\ \\(32,691-35,564)^2=8,254,129\\ \\(33,664-35,564)^2=3,610,000\\ \\(35,166-35,564)^2=158,404\\ \\(35,901-35,564)^2=113,569\\ \\(39,338-35,564)^2=14,243,076\\ \\(41,027-35,564)^2=29,844,369

Now,

\sigma =\sqrt{\dfrac{75,627,572}{7}}\approx 3,286

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Answer:

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Step-by-step explanation:

Given Mr. Johnson is working on constructing a square table for his classroom. He positioned his design on a coordinate grid, as shown. Mr. Johnson will need to put a brace through each diagonal of the table in order to secure the table's stability.

Now, if Johnson use more than one brace then we have to prove that the braces will intersect at a right angle.

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\text{Slope of BD=}\frac{y_2-y_1}{x_2-x_1}=\frac{2-(-5)}{4-(-3)}=\frac{7}{7}=1

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As we know, In a coordinate plane, the slopes of perpendicular lines are opposite reciprocals of each other i.e their product is equals to -1.

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