Which values in this data set are outliers?61,53,21,48,78,84,56,52,58,62,63

Based on these calculations, the outliers in the data set are 21 and 84

 To determine which values in your data set are outliers, we typically use statistical measures such as the interquartile range (IQR). Here are the steps to find the outliers:

1. Arrange the data values in ascending order: 21, 48, 52, 53, 56, 58, 61, 62, 63, 78, 84

2. Find the median (the middle value) of the data set. When there are an odd number of values, the median is the center number. In this case, the median is 58.

3. Divide the ordered data set into two halves: one before and one after the median value. - Lower half (before the median): 21, 48, 52, 53, 56 - Upper half (after the median): 61, 62, 63, 78, 84

4. Find the median of the lower half, which is called the lower quartile (Q1). The median of the lower half is 52. 5. Find the median of the upper half, which is called the upper quartile (Q3). The median of the upper half is 63.

6. Calculate the interquartile range by subtracting the lower quartile from the upper quartile: IQR = Q3 - Q1 = 63 - 52 = 11.

7. Determine the outlier cutoff points: - The lower bound for outliers is Q1 - 1.5 * IQR = 52 - 1.5 * 11 = 52 - 16.5 = 35.5. - The upper bound for outliers is Q3 + 1.5 * IQR = 63 + 1.5 * 11 = 63 + 16.5 = 79.5.

Any value lower than 35.5 (lower bound) or higher than 79.5 (upper bound) is considered an outlier. Thus, looking at the values in the data set: - The value 21 is below the lower bound, which means it's an outlier. - The value 84 is above the upper bound, which means it's also an outlier.