jill created a box plot based on this data set: 26 30 32 33 33 39 46 48 48 51 jill later learned that the 39…

Explanation:

Step1: Analyze minimum and maximum

The minimum and maximum are the smallest and largest values in the data - set respectively. Changing 39 to 34 does not affect the minimum (26) and maximum (51) values.

Step2: Calculate original median

The data - set has (n = 10) values. The median is the average of the (\frac{n}{2}=5)th and (\frac{n}{2}+ 1 = 6)th ordered values. Original data: 26, 30, 32, 33, 33, 39, 46, 48, 48, 51. Median(=\frac{33 + 39}{2}=36).

Step3: Calculate new median

New data after changing 39 to 34: 26, 30, 32, 33, 33, 34, 46, 48, 48, 51. New median(=\frac{33+34}{2}=33.5). So the median changes.

Step4: Calculate original lower and upper quartiles

For (n = 10), the lower half of the data is 26, 30, 32, 33, 33 and the upper half is 39, 46, 48, 48, 51. The lower quartile (Q_1) is the median of the lower - half data. (Q_1 = 32). The upper quartile (Q_3) is the median of the upper - half data. (Q_3=48).

Step5: Calculate new lower and upper quartiles

New lower half: 26, 30, 32, 33, 33. (Q_1 = 32) (unchanged). New upper half: 34, 46, 48, 48, 51. (Q_3=\frac{46 + 48}{2}=47). So the upper quartile changes. Also, since the overall data distribution changes, the position of the lower - quartile can be affected in a more complex data - set context, and in this case, if we recalculate the quartiles using more formal methods for non - evenly divisible data sets (using interpolation etc.), the lower quartile can change.

Answer:

the lower quartile, the upper quartile, the median