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22.08.2022 12:37
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Given the data 12, 39, 21, 18, 24, 17, 12, 25: a. what is the outlier in the data?

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?
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wwall7
wwall7
4,5(66 marks)

(a) No outliers

(b) 21

(c) 21

Explanation:

(a)

The given data set is ย 

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) ย 

Q_1=\dfrac{12+17}{2}=14.5

Q_3=\dfrac{24+25}{2}=24.5

IQR=Q_3-Q_1=24.5-14.5=10

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

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.

Mean=\dfrac{\text{Sum of all observations}}{\text{Number of observations}}

Mean=\dfrac{12+12+17+18+21+24+25+39}{8}

Mean=\dfrac{168}{8}

Mean=21

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.

IIHarmonyII
IIHarmonyII
4,5(8 marks)

$11,000

Explanation:

Based on the information given What will be the MAXIMUM AMOUNT OF THE CHARITABLE CONTRIBUTION ALLOWABLE as an itemized deduction on Deet's income tax return will be the amount of $11,000 which represent the amount the art value that Deet donated to the local art museum which was valued at $11,000.

Therefore the maximum amount of the charitable contribution allowable as an itemized deduction on Deet's income tax return is $11,000

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