contestada

Given the data 12, 39, 21, 18, 24, 17, 12, 25:
a. what is the outlier in the data?
b. what is the mean with the outlier?
c. what is the mean without the outlier?

Respuesta :

MissPhiladelphia
12, 39, 21, 18, 24, 17, 12, 25:
The outlier in the data is 39The mean with the outlier in the data is 21The mean without the outlier is 18.42


Thank you for your question. Please don't hesitate to ask in Brainly your queries. 

Answer:

(a) No outliers

(b) 21

(c) 21

Explanation:

(a)

The given data set is  

12, 39, 21, 18, 24, 17, 12, 25

Arrange the data in ascending order.

12, 12, 17, 18, 21, 24, 25, 39

Divide the data in 4 equal parts.

(12, 12), (17, 18), (21, 24), (25, 39)  

[tex]Q_1=\dfrac{12+17}{2}=14.5[/tex]

[tex]Q_3=\dfrac{24+25}{2}=24.5[/tex]

[tex]IQR=Q_3-Q_1=24.5-14.5=10[/tex]

[tex][Q_1-1.5(IQR),Q_3+1.5(IQR)]=[14.5-1.5(10),24.5+1.5(10)]=[-0.5,39.5][/tex]

All the data value lie in the interval [-0.5,39.5].

Therefore the given data set have no outliers.

(b)

Mean of the data with the outliers.

[tex]Mean=\dfrac{\text{Sum of all observations}}{\text{Number of observations}}[/tex]

[tex]Mean=\dfrac{12+12+17+18+21+24+25+39}{8}[/tex]

[tex]Mean=\dfrac{168}{8}[/tex]

[tex]Mean=21[/tex]

Therefore, mean of the data with the outliers is 21.

(c)

Since the given data set has no outlier, therefore, the mean of the data with the outliers and without outliers is same, i.e., 21.