Ask a New Question
Menu

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)/

1 answer

To find the means of the original dataset and the new dataset after removing the value "70," we will follow these steps:

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

    • Calculate the sum of the original dataset: \[ 0 + 10 + 15 + 4 + 70 + 15 + 18 + 20 + 6 + 8 + 10 + 12 + 15 + 18 + 20 + 2 + 35 + 40 + 10 = 328 \]

    • Count the number of data points in the original dataset: There are 19 data points.

    • Calculate the mean of the original dataset: \[ \text{Mean} = \frac{\text{Sum}}{\text{Count}} = \frac{328}{19} \approx 17.2632 \] Rounding to one decimal place, the mean is 17.3.

  2. New dataset (after removing 70): {0, 10, 15, 4, 15, 18, 20, 6, 8, 10, 12, 15, 18, 20, 2, 35, 40, 10}

    • Calculate the sum of the new dataset: \[ 0 + 10 + 15 + 4 + 15 + 18 + 20 + 6 + 8 + 10 + 12 + 15 + 18 + 20 + 2 + 35 + 40 + 10 = 279 \]

    • Count the number of data points in the new dataset: There are now 18 data points.

    • Calculate the mean of the new dataset: \[ \text{Mean} = \frac{\text{Sum}}{\text{Count}} = \frac{279}{18} \approx 15.5 \]

So, the final results are:

  • Mean of the original dataset: 17.3
  • Mean of the new dataset (after removing 70): 15.5