Question

Remember when I asked you your age on the first day? Well, here is a subset of the data that I obtained: 18 18 19 19 19 19 20 21 22 23 25 28 33 1) Find the mean, nadian, and mode of the data. Mean = 21.85 Median = 20 Mode = 19 2) Pind the standard deviation, variance, and range of the data. Standard deviation = 4.47 Variance = 19.98 Range = 15 3) Find the x-scores of the largest and smallest data values. Which one is more unusual? -score => z=x -u - Z The smallest (negative value in this case) is more unusual smallest s 18- 21.85 4:47 4.47 - 0.8613 (negative 4) Find the five number summary of the data y alue means its - Min = 18 below mean ) 20.86 Q1 = 19 Med = 20 Q3 = 24 Max = 33 5) Calculate the upper and lower limits for outliers. Circle any data values above that fall outside these limita, largest = 33-21.850 Wby to 66 6. tl positive value means IQR Q3 - Qi 21-19

Answer 1

Solution-:

By using r-software

> x=c(18,18,19,19,19,19,20,21,22,23,25,28,33);x
[1] 18 18 19 19 19 19 20 21 22 23 25 28 33
> #(1)
> #for mean
> Mean=mean(x);Mean
[1] 21.84615
> #for median
> med=median(x);med
[1] 20
> #for mode
> tx=table(x);
> m=which(tx==max(tx))
> stx=sort(unique(x))
> Mode=stx[m];
> Mode
[1] 19
> #(2)
> #for variance
> n=13
> v=var(x);v
[1] 19.97436
> var=((n-1)/n)*v;var
[1] 18.43787
> sd=sqrt(var);sd # Standard Deviation
[1] 4.293934
> #for range
> min=min(x);min
[1] 18
> max=max(x);max
[1] 33
> range=max-min;range
[1] 15
> # (3)
> #Z-score for smallest value
> Zscoremin=(18-21.85)/4.29;Zscoremin
[1] -0.8974359
> # Here, Z-scoremin is unusual.
> #Z-score for largest value
> Zscoremax=(33-21.85)/4.29;Zscoremax
[1] 2.599068
> #Here, Z-scoremax is unusual.
> #In general, Z-score lower than -1.96 or higher than 1.96 are considered as unusual.
> #(4)For five number summary
> Q1=quantile(x,0.25);Q1 # first quartile
25%
19
> Q3=quantile(x,0.75);Q3 # Third quartile
75%
23
> # min=18,Q1=19,Q2=med=20, Q3=23,max=33
> #(5) For IQR
> IQR=Q3-Q1;IQR
75%
4

R-Program Code

x=c(18,18,19,19,19,19,20,21,22,23,25,28,33);x
#(1)
#for mean
Mean=mean(x);Mean
#for median
med=median(x);med
#for mode
tx=table(x);
m=which(tx==max(tx))
stx=sort(unique(x))
Mode=stx[m];
Mode
#(2)
#for variance
n=13
v=var(x);v
var=((n-1)/n)*v;var
sd=sqrt(var);sd # Standard Deviation
#for range
min=min(x);min
max=max(x);max
range=max-min;range
# (3)
#Z-score for smallest value
Zscoremin=(18-21.85)/4.29;Zscoremin
# Here, Z-scoremin is unusual.
#Z-score for largest value
Zscoremax=(33-21.85)/4.29;Zscoremax
#Here, Z-scoremax is unusual.
#In general, Z-score lower than -1.96 or higher than 1.96 are considered as unusual.
#(4)For five number summary
Q1=quantile(x,0.25);Q1 # first quartile
Q3=quantile(x,0.75);Q3 # Third quartile
# min=18,Q1=19,Q2=med=20, Q3=23,max=33
#(5) For IQR
IQR=Q3-Q1;IQR