Q. 3.159 - Elementary Statistics

Question

We have provided simple data sets for you to practice finding the descriptive measures discussed in this section. For each data set.

Obtain the quartiles, determine the inter quartile range, find the five-number summary.

$1,2,3,4$

Step-by-Step Solution

Answer

The value of Least value is$=1$,

The value of first quartile is $1.5$, The value of second quartile is $2.5$, The value of third quartile is$3.5$

The value of Highest value is $4$ And The value of Inter quartile is $2$

And Boxplots is given below

Step 1: Given information

We have been given that 

$1,2,3,4$

Now we find quartiles, inter quartiles and five number summary

Step 2: Explanation

The known data is arranged in ascending order is,

$1,2,3,4$

The least value, also known as the minimum, is a descriptive statistics that represents the smallest 

Number within the data set,

So, Least value$=1$

The lower quartiles, also known as $Q_1$is a deceptive statistics that represents the number in the

Middle of the lower half of the data set,

So, $Q_1=1.5$

The median, also known as  $Q_2$, is a deceptive statistics that represents the number in the middle

Of all the data within the data set,

Median$\Rightarrow Q_2=2.5$

The upper quartile, also known as$Q_3$, is deceptive statistics that represents the number in the

Upper half of the data set,

So, $Q_3=3.5$

The upper extreme, also known as the maximum, is a descriptive statistics that represent the 

Largest number within the data set.

Highest value$=4$

Step 3: Find Inter quartile and draw boxplots

The range of values that resides in the middle of the scores,
$Interquartile=Q_3-Q_1$

$\Rightarrow 3.5-1.5=2$

Now we draw a Boxplots,