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The director of a local Parks and Recreation department is interested in the number of hours kids spend outside each week. She surveys a group of 19 kids in her town and asks them how many hours they spent outside last week. Her results follow.

{0,10,15,4,70,15,18,20,6,8,10,12,15,18,20,2,35,40,10}

The director decides to remove the data value “70” since it is a lot larger than the rest of the data values. Calculate the mean of the original dataset and the mean of the new dataset after “70” is removed. Round your answers to one decimal place.(1 point)
The mean of the original dataset is
. The mean of the new dataset after “70” is removed is
.
Incorrect

The mean of a dataset is the average. First, add all the values in the dataset. Then, divide by the number of values.
Subtract 70 from the total of the original dataset. Then, divide by the number of values, which is now 18 instead of 19.

1 answer

To calculate the mean of the original dataset and the new dataset after removing the value "70," we can follow these steps:

Step 1: Calculate the mean of the original dataset.

Original dataset: {0, 10, 15, 4, 70, 15, 18, 20, 6, 8, 10, 12, 15, 18, 20, 2, 35, 40, 10}

  1. First, add the values together:

\[ 0 + 10 + 15 + 4 + 70 + 15 + 18 + 20 + 6 + 8 + 10 + 12 + 15 + 18 + 20 + 2 + 35 + 40 + 10 = 0 + 10 + 15 + 4 + 70 + 15 + 18 + 20 + 6 + 8 + 10 + 12 + 15 + 18 + 20 + 2 + 35 + 40 + 10 = 460 \]

  1. Next, divide by the number of values in the dataset. There are 19 values:

\[ \text{Mean} = \frac{460}{19} \approx 24.2 \]

Step 2: Calculate the mean of the new dataset after removing "70."

New dataset: {0, 10, 15, 4, 15, 18, 20, 6, 8, 10, 12, 15, 18, 20, 2, 35, 40, 10}

  1. Add the new values together:

\[ 0 + 10 + 15 + 4 + 15 + 18 + 20 + 6 + 8 + 10 + 12 + 15 + 18 + 20 + 2 + 35 + 40 + 10 = 0 + 10 + 15 + 4 + 15 + 18 + 20 + 6 + 8 + 10 + 12 + 15 + 18 + 20 + 2 + 35 + 40 + 10 = 427 \]

  1. Next, divide by the new number of values. There are now 18 values:

\[ \text{Mean} = \frac{427}{18} \approx 23.7 \]

Final Answers:

  • The mean of the original dataset is 24.2.
  • The mean of the new dataset after “70” is removed is 23.7.