Question

for a science project, rhianna set out to study how long people can hold their breath. rhianna asked some classmates to hold their breath for as long as they could. here are the results, given in seconds: 73 61 65 82 68 18 70 65 76 85 rhianna notices that there is an outlier in the data and decides to remove it. how does removing the outlier affect the following measures? mean median mode range increases decreases remains the same

Explanation:

Step1: Identify the outlier

The data set is 73, 61, 65, 82, 68, 18, 70, 65, 76, 85. The outlier is 18 as it is far from other values.

Step2: Calculate the mean before removing the outlier

The sum of all values is \(73 + 61+65 + 82+68+18+70+65+76+85=663\). There are \(n = 10\) values. The mean \(\bar{x}_1=\frac{663}{10}=66.3\).

Step3: Calculate the mean after removing the outlier

The sum of the remaining 9 - values is \(663 - 18=645\). The new mean \(\bar{x}_2=\frac{645}{9}\approx71.67\). So the mean increases.

Step4: Calculate the median before removing the outlier

Arrange the data in ascending - order: 18, 61, 65, 65, 68, 70, 73, 76, 82, 85. Since \(n = 10\) (even), the median \(M_1=\frac{68 + 70}{2}=69\).

Step5: Calculate the median after removing the outlier

Arrange the remaining 9 values in ascending - order: 61, 65, 65, 68, 70, 73, 76, 82, 85. Since \(n = 9\) (odd), the median \(M_2 = 70\). So the median increases.

Step6: Determine the mode

The mode of the original data set is 65 (it appears twice). After removing the outlier, the mode is still 65. So the mode remains the same.

Step7: Calculate the range before removing the outlier

The range \(R_1=85 - 18 = 67\).

Step8: Calculate the range after removing the outlier

The range \(R_2=85 - 61 = 24\). So the range decreases.

Answer:

Mean: Increases
Median: Increases
Mode: Remains the same
Range: Decreases