Step 1

It is an important part of statistics . It is widely used .

Mean is defined as the average.

Median is defined as the middl

emost value of the observation such that half of the value lies above it and half below it .

Mode is defined as that value which has the maximum frequency .

Step 2

a)

R CODE :

\(x=c(410,\ 450,\ 435,\ 375,\ 395,\ 255,\ 290,\ 105,\ 410,\ 385)\)

mean(x)

median(x)

OUTPUT :

\(\Rightarrow x=c(410,\ 450,\ 435,\ 375,\ 395,\ 255,\ 290,\ 105,\ 410,\ 385)\)

\(\Rightarrow mean(x)\)

\(\left[1\right] 351\)

\(\Rightarrow median(x)\)

\(\left[1\right] 390\)

There is no mode as all the values have same frequency equal to 1

The required mean is 351 and median is 390

b)

R CODE :

\(quantile(x,0.25)\)

\(quantile(x,0.75)\)

OUTPUT :

\(\Rightarrow quantile(x,0.25)\)

\(25\%\)

311.25

\(\Rightarrow quantile(x,0.75)\)

\(75\%\)

410

The first quartile of the data is 311.25

The third quartile of the data is 410

c)

Median is the best measure of central tendency as it tells the location of the central value .