Answered

At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Below are survival times (in days) of 13 guinea pigs that were injected with a bacterial infection in a medical study:
91 83 84 79 91 93 95 97 97 120 101 105 98


Are there any outliers in the data set above? Use the 1.5 IQR rule to check.


Q1 =


Q3 =


IQR =


IQR(1.5) =


Q3 + IQR(1.5) =
(Upper outlier)

Q1 - IQR(1.5) =
(Lower outlier)

Name any outliers in the set of data:

Sagot :

MrRoyal

Outliers are data that are relatively far from other data elements.

The dataset has an outlier and the outlier is 120

The dataset is given as:

  • 91 83 84 79 91 93 95 97 97 120 101 105 98

Sort the dataset in ascending order

  • 79 83 84 91 91 93 95 97 97 98 101 105 120

The lower quartile (Q1)

The Q1 is then calculated as:

[tex]Q1 = \frac{N +1}{4}th[/tex]

So, we have:

[tex]Q1 = \frac{13 +1}{4}th[/tex]

[tex]Q1 = \frac{14}{4}th[/tex]

[tex]Q1 = 3.5th[/tex]

This is the average of the 3rd and the 4th element

[tex]Q1 = \frac{1}{2} \times (84 + 91)[/tex]

[tex]Q1 = 87.5[/tex]

The upper quartile (Q3)

The Q3 is then calculated as:

[tex]Q3 = 3 \times \frac{N +1}{4}th[/tex]

So, we have:

[tex]Q3 = 3 \times \frac{13 +1}{4}th[/tex]

[tex]Q3 = 3 \times 3.5th[/tex]

[tex]Q3 = 10.5th[/tex]

This is the average of the 10th and the 11th element.

[tex]Q_3 =\frac12 \times (98 + 101)[/tex]

[tex]Q_3 =99.5[/tex]

The interquartile range (IQR)

The IQR is then calculated as:

[tex]IQR = Q_3 -Q_1[/tex]

[tex]IQR = 99.5 - 87.5[/tex]

[tex]IQR = 12[/tex]

Also, we have:

[tex]IQR(1.5) = 12 \times 1.5[/tex]

[tex]IQR(1.5) = 18[/tex]

The outlier range

The lower and the upper outlier range are calculated as follows:

[tex]Lower = Q_1 - IQR(1.5)[/tex]

[tex]Lower = 87.5- 18[/tex]

[tex]Lower = 69.5[/tex]

[tex]Upper = Q_3 + IQR(1.5)[/tex]

[tex]Upper = 99.5 + 18[/tex]

[tex]Upper = 117.5[/tex]

120 is greater than 117.5.

Hence, the dataset has an outlier and the outlier is 120

Read more about outliers at:

https://brainly.com/question/9933184

We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.