Question

Simple data sets have been given for you to try locating the descriptive metrics mentioned in this section. For each data set separately.

(a) Calculate the quartiles,

(b) calculate the interquartile range

(c)compile a five-number summary.

$1,2,3,4,5,6,1,2,3,4,5,6$

Short answer

(a) This question's quartiles are$Q_1=2,Q_2=3.5,Q_3=5$

(b) The interquartile range (IQR) is localid="1651231768548" $3$

(c) This question's five-number summary is Least value.localid="1651231793811" $=1$localid="1650963397893" $Q_1=2,Q_2=3.5,Q_3=5$The most valuablelocalid="1651231816553" $=6$, Boxplots are shown below.

Step-by-step solution

Part(a) Step 1: Given information

We have been given that,

The data set consists of$1,2,3,4,5,6,1,2,3,4,5,6$

Part(a) Step 2:Explanation

We'll now sort the numbers in ascending order.

As a result, the numbers in the data set appear like this.$1,1,2,2,3,3,4,4,5,5,6,6$

Quartiles are numerical values that divide data into four equal halves.

The lower quartiles, often known as $Q_1$, is a misleading statistic that depicts the number of people in the bottom half of the population.

In the lower half of the data set, in the middle,

So, $Q_1=2$

The median, often known as$Q_2$, is a misleading statistic that indicates the number in the midpoint of a range of values.

Out of all the data in the collection,

So, $Q_2=3.5$

The upper quartile, often known as$Q_3$, is a misleading statistic that represents the number of people in the top quartile.

The data set's upper half,

So, localid="1650771871507" $Q_3=5$

Part(b) Step 1: Given information

We have been given that,

In the midst of the scores, there is a range of values.

Part(b) Step 2: Explanation

Now, using the formula to get the interquartile range,

$IQR=Q_3-Q_1$

Now, enter the value in the formula above.

$IQR=Q_3-Q_1=5-2=3$

Part(c) Step 1: Given information

We have been given that,

Arrange the supplied data collection in ascending order,

The$1,1,2,2,3,3,4,4,5,5,6,6$

Part(c) Step 2: Explanation

A five-number summary is a method of summary a dataset using the five values listed below:

At the very least, The first quarter is made up of people who are in their early twenties The average, The third quarter is made up of people who are between the ages of 18 and The maximum amount of the smallest number, often known as the minimum, is a descriptive statistic.

Within the data set, there is a number,

As a result, Least Value$=1$

The upper extreme, often known as the maximum, is a descriptive statistic that represents the highest point in a data set.

The data set's largest number.

Consequently, the highest value$=6$

$Q_1=2,Q_2=3.5,Q_3=5$

Now we're going to make Boxplots.