Question

question 11 (multiple choice worth 2 points)
(effects of changes in data mc)
the ages of a group of teachers are listed.
25, 32, 33, 35, 41, 43, 45, 48, 52, 55, 60, 62
if another teacher with an age of 45 is added to the data, how would the mean be impacted?
the value of the mean would remain the same at about 41.
the value of the mean would remain the same at about 44.
the mean would increase in value to about 47.
the mean would decrease in value to about 42.

Explanation:

Step1: Calculate the original sum

The original data set is \(25, 32, 33, 35, 41, 43, 45, 48, 52, 55, 60, 62\). The number of data points \(n = 12\).
Sum of original data: \(25+32 + 33+35+41+43+45+48+52+55+60+62\)
\(=25+(32 + 33)+(35)+(41)+(43)+(45)+(48)+(52)+(55)+(60)+(62)\)
\(=25 + 65+35+41+43+45+48+52+55+60+62\)
\(=(25 + 65)+(35)+(41)+(43)+(45)+(48)+(52)+(55)+(60)+(62)\)
\(=90+35+41+43+45+48+52+55+60+62\)
\(=(90 + 35)+(41)+(43)+(45)+(48)+(52)+(55)+(60)+(62)\)
\(=125+41+43+45+48+52+55+60+62\)
\(=(125 + 41)+(43)+(45)+(48)+(52)+(55)+(60)+(62)\)
\(=166+43+45+48+52+55+60+62\)
\(=(166 + 43)+(45)+(48)+(52)+(55)+(60)+(62)\)
\(=209+45+48+52+55+60+62\)
\(=(209 + 45)+(48)+(52)+(55)+(60)+(62)\)
\(=254+48+52+55+60+62\)
\(=(254 + 48)+(52)+(55)+(60)+(62)\)
\(=302+52+55+60+62\)
\(=(302 + 52)+(55)+(60)+(62)\)
\(=354+55+60+62\)
\(=(354 + 55)+(60)+(62)\)
\(=409+60+62\)
\(=(409 + 60)+62\)
\(=469+62 = 531\)

Step2: Calculate the original mean

Original mean \(\bar{x}=\frac{531}{12}=44.25\approx44\)

Step3: Calculate the new sum and new mean

After adding a new data point \(45\), the new sum is \(531 + 45=576\)
The new number of data points \(n'=12 + 1=13\)
New mean \(\bar{x}'=\frac{576}{13}\approx44.31\approx44\)

Answer:

The value of the mean would remain the same at about 44. (Option: The value of the mean would remain the same at about 44)