Q. 3.165 - Elementary Statistics

Question

For you to practice finding the descriptive measures mentioned in this part, we have provided simple data sets. Each data set separately.

a) Calculate the quartiles

b) calculate the interquartile range

c)recognize the five-number summary

$1,2,3,4,5,6,7$

Step-by-Step Solution

Answer

(a) This question's quartiles are$Q_1=2,Q_2=4,Q_3=6$

(b) The interquartile range (IQR) is$3$

(c) Least value is the five-number summary.$=1$$Q_1=2,Q_2=4,Q_3=6$The most valuable$=7$

And the boxplots are as follows:

Part(a) Step 1: Given information

We have been given that,

The data set consists of$1,2,3,4,5,6,7$

Part(a) Step 2: Explanation

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, $Q_2=4$

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, $Q_3=6$

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, fill in the values in the formulas above.

$IQR=Q_3-Q_1=6-2=4$

Part(c) Step 1: Given information

We have been given that,

The data set consists of$1,2,3,4,5,6,7$

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 median, the first quartile The maximum is in the third quartile.

The smallest Number within the data collection is represented by the least value, often known as the minimum.

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$=7$

And $Q_1=2,Q_2=4,Q_3=6$

Now we're going to make Boxplots.