Question

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

Answer 1

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,

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