Loren’s friends jump as far as they can and record their results in inches. Their results include the observations 42, 47, 50, 42, 45, 41, 49, 51, and 44. Which number, if added to the dataset, would represent an outlier in the data
The outlier in a dataset is typically defined as a value that is significantly higher or lower than the rest of the values. In this case, the numbers in the dataset are: 42, 47, 50, 42, 45, 41, 49, 51, and 44.
To determine which number would represent an outlier in this dataset, we can calculate the median and the interquartile range (IQR). The median of the dataset is the middle value when the numbers are arranged in ascending order. In this case, the numbers when arranged in ascending order are: 41, 42, 42, 44, 45, 47, 49, 50, 51. The median is the middle value, which is 44.
Next, we need to calculate the IQR. To do this, we first need to find the lower quartile (Q1) and the upper quartile (Q3). The lower quartile is the median of the lower half of the data, and the upper quartile is the median of the upper half of the data.
In this case:
Lower quartile (Q1) = median of 41, 42, 42, 44 = 42
Upper quartile (Q3) = median of 47, 49, 50, 51 = 49
IQR = Q3 - Q1 = 49 - 42 = 7
Now, we can use the IQR to determine the lower and upper limits for outliers. The lower limit is Q1 - 1.5 * IQR and the upper limit is Q3 + 1.5 * IQR.
Lower limit = 42 - 1.5 * 7 = 31.5
Upper limit = 49 + 1.5 * 7 = 59.5
Any number outside of the range 31.5 to 59.5 would be considered an outlier in this dataset. In this case, none of the numbers provided in the dataset fall outside of this range.