Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 11 Data Analysis and Statistics - 11.2 Apply Transformations to Data - 11.2 Exercises - Quiz for Lessons 11.1.11.2 - Page 755: 3

Answer

See below.

Work Step by Step

The mean of $n$ numbers is the sum of the numbers divided by $n$. The median of $n$ is the middle number of the numbers when they are in order (and the mean of the middle $2$ numbers if $n$ is even). The mode of $n$ numbers is the number or numbers that appear(s) most frequently. Hence here the mean: $\frac{43+44+45+47+48+55+56+56}{8}=49.25$, the median is the mean of the middle items in the sequence $ 43,44,45, 47, 48, 55,56,56$, which is: $(47+48)/2=47.5$, the mode is $56$. The range is the difference between the largest and the smallest data value. The standard deviation of $x_1,x_2,...,x_n$ is (where $\overline{x}$ is the mean of the data values): $\sqrt{\frac{(x_1-\overline{x})^2+(x_2-\overline{x})^2+...+(x_n-\overline{x})^2}{n}}$. Hence here the range is: $56-43=13$ and the standard deviation is: $\sqrt{\frac{(43-49.25)^2+(44-49.25)^2+...+(56-49.25)^2}{8}}\approx5.127$
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