the data - set contains six values: 10, 12, 12, 16, 14, 16. which of the following is an accurate statement…
the data - set contains six values: 10, 12, 12, 16, 14, 16. which of the following is an accurate statement when 16 is added to the data - set? a. the median does not change. b. the mean decreases. c. the mean does not change.
Answer
Explanation:
Step1: Calculate original mean
The original data - set is (10,12,12,14,16,16). The mean (\bar{x}_1=\frac{10 + 12+12+14+16+16}{6}=\frac{80}{6}=\frac{40}{3}\approx13.33).
Step2: Calculate original median
Arrange the original data - set in ascending order: (10,12,12,14,16,16). Since (n = 6) (even), the median (M_1=\frac{12 + 14}{2}=13).
Step3: Add 16 to the data - set and calculate new mean
The new data - set is (10,12,12,14,16,16,16). The new mean (\bar{x}_2=\frac{10 + 12+12+14+16+16+16}{7}=\frac{96}{7}\approx13.71). Since (\frac{96}{7}>\frac{40}{3}), the mean increases.
Step4: Add 16 to the data - set and calculate new median
Arrange the new data - set in ascending order: (10,12,12,14,16,16,16). Since (n = 7) (odd), the median (M_2 = 14).
Since the original median is 13 and the new median is 14, the median changes. Since the mean increases from (\frac{40}{3}) to (\frac{96}{7}), options B and C are incorrect.