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the dataset below represents the heights of trees(in inches) 13, 82, 83, 95, 92, 98, 96. How many outliers are in this data set?

Sagot :

Zebutic

Answer:

3

Step-by-step explanation:

There are 3 outliers. 13, 82, 83. These outliers are marginally off by the rest of the set.

There is one outlier in the data. The value of outlier is 13.

What is an outlier?

An outlier is an observation that lies an abnormal distance from other values in a random sample from a population. It is a value that "lies outside" (is much smaller or larger than) most of the other values in a set of data. The outliers can be found from median and quartile range.

For the given situation,

The heights of trees(in inches) are 13, 82, 83, 95, 92, 98, 96.

Arrange them in ascending order,

⇒ [tex]13, 82, 83, 92, 95, 96, 98[/tex]

Here, median = 95

So, first quartile Q₁ = 82

third quartile, Q₃ = 96

Interquartile range, IQR = Q₃ - Q₁

⇒ [tex]96-82[/tex]

⇒ [tex]14[/tex]

Now, [tex]IQR(1.5)=14(1.5)[/tex]

⇒ [tex]21[/tex]

Then, high value = Q₃+1.5 IQR

⇒ [tex]96+21[/tex]

⇒ [tex]117[/tex]

Low value = Q₁-1.5 IQR

⇒ [tex]82-21[/tex]

⇒ [tex]61[/tex]

From the data, the value of outlier should lie less than 61 and greater than 117.

Hence we can conclude that there is one outlier in the data. The value of outlier is 13.

Learn more about outliers here

https://brainly.com/question/3253658

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