Math / Data & Statistics

QuestionWhat impact does deleting the data value 18 have on the mean of the dataset $(19,18,22,19,18,22,17,20,18)$ ? Round your answer to the nearest tenth. (1 point) Dataset 1 has a mean of 19.2, and dataset 2 has a mean of 17.3. Dataset 1 has a mean of 19.2, and dataset 2 has a mean of 19.4.
The mean of the original dataset is 18 and did not change with the deletion of the data value.
The mean of the original dataset is 19 and did not change with the deletion of the data value.

Studdy Solution

STEP 1

1. The original dataset is $(19, 18, 22, 19, 18, 22, 17, 20, 18)$ .
2. We need to calculate the mean of the original dataset.
3. We need to calculate the mean of the dataset after deleting one occurrence of the value 18.
4. The impact on the mean is determined by the difference between the original mean and the new mean.

STEP 2

1. Calculate the mean of the original dataset.
2. Delete one occurrence of the value 18 and calculate the new mean.
3. Determine the impact on the mean.

STEP 3

Calculate the mean of the original dataset.
The original dataset is $(19, 18, 22, 19, 18, 22, 17, 20, 18)$ .
Sum of the original dataset:
$19 + 18 + 22 + 19 + 18 + 22 + 17 + 20 + 18 = 173$
Number of data points in the original dataset:
$9$
Mean of the original dataset:
$\frac{173}{9} \approx 19.2$

STEP 4

Delete one occurrence of the value 18 and calculate the new mean.
The new dataset is $(19, 22, 19, 18, 22, 17, 20, 18)$ .
Sum of the new dataset:
$19 + 22 + 19 + 18 + 22 + 17 + 20 + 18 = 155$
Number of data points in the new dataset:
$8$
Mean of the new dataset:
$\frac{155}{8} \approx 19.4$

STEP 5

Determine the impact on the mean.
Original mean: $19.2$
New mean: $19.4$
The mean increased by:
$19.4 - 19.2 = 0.2$
The impact of deleting the data value 18 on the mean is an increase of $0.2$ .

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