Chapter 1
Basic Operations on Real Numbers
Addition, Subtraction, Multiplication, and Division of Real Numbers
Examples (Open R/RStudio and type into Console)
3+5
3-5
3.25*4.125
15/3
# three raised to fourth power can be evaluated as:
3^4
# Square root operation: square root of 16 can be evaluated as
sqrt(16)Scientific-Like Notation in R
# 1250 can be displayed in R as 1.25e+3: justification: 1.25*10^3=1.25*1000
# 0.000125 can be displayed in R as 1.25e-4; while using the following 1.25*10^(-4) calculation by hand.Use R or RStudio for exercises listed below:
Evaluate expression and round each to the nearest hundredth:
\[ \frac{179.5-173}{2.9} \]
\[ \frac{179.5-180}{\frac{2.8}{\sqrt{40}}} \]
\[ \frac{(1-10)^2+(4-10)^2+(11-10)^2+(13-10)^2}{4-1} \]
Convert to percent
\[ \frac{3}{8} \]
\[ 0.2345 \]
Evaluate the following standarized z scores:
\[ z_{1}=\frac{145-175}{6}= \] \[ z_{2}=\frac{236-175}{6}= \] \[ z_{3}=\frac{183-175}{6}= \] \[ z_{4}=\frac{145-175}{6}= \]
Here is your R syntax followed by numerical answer:
(247-175)/6## [1] 12(236-175)/6## [1] 10.16667(183-175)/6## [1] 1.333333(145-175)/6## [1] -5Calculate above z-scores at once by using the following syntax
x <-c(247,236,183,145)
mean <-175
sd <-6
(x-mean)/sd## [1] 12.000000 10.166667 1.333333 -5.000000