Mathematics: Suppose the following data set represents the starting salaries for the population of teachers from seven states: $41,027, $35,901, $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

can you give me more? step-by-step explanation:...

Suppose the following data set represents the

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katyym80

03.01.2022

Mathematics

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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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Suppose the following data set represents the starting salaries for the population of teachers from seven states: $41,027, $35,901, $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

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