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(a)The height of students in inches that were recorded were5 6 7 77 7 8 810 10 11 15Are there any outliers?AYesBNo

Question

(a)The height of students in inches that were recorded were5 6 7 77 7 8 810 10 11 15Are there any outliers?AYesBNo

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Solution

To determine if there are any outliers in the data, we can use the Interquartile Range (IQR) method. Here are the steps:

  1. First, arrange the data in ascending order: 5, 6, 7, 7, 7, 8, 8, 10, 10, 11, 15, 77.

  2. Next, find the median (Q2). Since we have 12 data points, the median is the average of the 6th and 7th values: (7+8)/2 = 7.5.

  3. Then, find the lower quartile (Q1), which is the median of the first half of the data. In this case, it's the average of the 3rd and 4th values: (7+7)/2 = 7.

  4. Find the upper quartile (Q3), which is the median of the second half of the data. It's the average of the 9th and 10th values: (10+11)/2 = 10.5.

  5. Calculate the IQR, which is Q3 - Q1: 10.5 - 7 = 3.5.

  6. Find the lower bound for outliers, which is Q1 - 1.5IQR: 7 - 1.53.5 = -2.25.

  7. Find the upper bound for outliers, which is Q3 + 1.5IQR: 10.5 + 1.53.5 = 15.75.

Any data points that are less than the lower bound or greater than the upper bound are considered outliers. In this case, the value 77 is an outlier. So, the answer is A: Yes, there are outliers.

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