Question

consider the following set of data: 350, 330, 310, 80, 410, 230, 310, 350, 410, 470... which two of the following values changed after removing the outlier? lower extreme, upper extreme, median, lower quartile, upper quartile

Explanation:

Step1: Identify the outlier

First, we identify the outlier in the data set. The data points are 350, 330, 310, 80, 410, 230, 310, 350, 410, 470. The value 80 is much smaller than the other values, so it is the outlier.

Step2: Analyze each measure before removing the outlier

• Lower extreme: The minimum value, which is 80.
• Upper extreme: The maximum value, which is 470.
• Median: First, we sort the data: 80, 230, 310, 310, 330, 350, 350, 410, 410, 470. There are 10 data points, so the median is the average of the 5th and 6th values: $\frac{330 + 350}{2} = 340$.
• Lower quartile (Q1): The median of the lower half (first 5 values: 80, 230, 310, 310, 330). The median of these 5 values is the 3rd value, which is 310.
• Upper quartile (Q3): The median of the upper half (last 5 values: 350, 350, 410, 410, 470). The median of these 5 values is the 3rd value, which is 410.

Step3: Analyze each measure after removing the outlier (80)

The new data set is: 230, 310, 310, 330, 350, 350, 410, 410, 470 (9 data points).

• Lower extreme: The new minimum value, which is 230 (changed from 80).
• Upper extreme: The maximum value is still 470 (no change).
• Median: For 9 data points, the median is the 5th value. Sorting the new data: 230, 310, 310, 330, 350, 350, 410, 410, 470. The 5th value is 350 (changed from 340).
• Lower quartile (Q1): The median of the lower half (first 4 values: 230, 310, 310, 330). The median of these 4 values is $\frac{310 + 310}{2} = 310$ (no change).
• Upper quartile (Q3): The median of the upper half (last 4 values: 350, 410, 410, 470). The median of these 4 values is $\frac{410 + 410}{2} = 410$ (no change).

Answer:

Lower extreme, Median