trevor is part of a team that entered a solar - powered car competition. during the race, participants drove…

trevor is part of a team that entered a solar - powered car competition. during the race, participants drove their solar - powered cars past a series of milestones. the dot plot shows the number of milestones the cars passed in the competition. race performance dot plot with x - axis labeled number of milestones passed from 1 to 10 and dots above values. trevors car passed 10 milestones and appeared to have won the race. however, he was disqualified for leaving the racecourse. how does excluding trevors performance from the data set affect the following measures? table with columns increases, decreases, remains the same and rows mean, median, mode, range

trevor is part of a team that entered a solar - powered car competition. during the race, participants drove their solar - powered cars past a series of milestones. the dot plot shows the number of milestones the cars passed in the competition. race performance dot plot with x - axis labeled number of milestones passed from 1 to 10 and dots above values. trevors car passed 10 milestones and appeared to have won the race. however, he was disqualified for leaving the racecourse. how does excluding trevors performance from the data set affect the following measures? table with columns increases, decreases, remains the same and rows mean, median, mode, range

Answer

Explanation:

Step1: Calculate the original mean

Let (x_i) be the number of milestones and (f_i) be the frequency of each value. The original data - set has values: (1) with frequency (1), (2) with frequency (3), (3) with frequency (4), (4) with frequency (5), (5) with frequency (2), (6) with frequency (1), (10) with frequency (1). The sum of the data - set (S_1=\sum_{i}x_if_i=1\times1 + 2\times3+3\times4 + 4\times5+5\times2+6\times1+10\times1=1 + 6+12 + 20+10+6+10 = 65). The number of data - points (n_1=1 + 3+4+5+2+1+1=17). The original mean (\bar{x}_1=\frac{S_1}{n_1}=\frac{65}{17}\approx3.82). After excluding Trevor's data ((x = 10)), (S_2=65 - 10=55) and (n_2=17 - 1 = 16). The new mean (\bar{x}_2=\frac{S_2}{n_2}=\frac{55}{16}=3.44). So the mean decreases.

Step2: Calculate the original median

The number of data - points (n_1 = 17) (odd). The median is the (\left(\frac{n_1 + 1}{2}\right))-th value. (\frac{17+1}{2}=9) - th value. Arranging the data in ascending order: (1,2,2,2,3,3,3,3,4,4,4,4,4,5,5,6,10), the median is (4). After excluding Trevor's data, (n_2 = 16) (even). The median is the average of the (\frac{n_2}{2})-th and (\left(\frac{n_2}{2}+1\right))-th values. (\frac{16}{2}=8) and (\frac{16}{2}+1 = 9). The ordered data set without (10) is (1,2,2,2,3,3,3,3,4,4,4,4,4,5,5,6). The median is (\frac{4 + 4}{2}=4). So the median remains the same.

Step3: Calculate the original mode

The mode is the most frequently occurring value. In the original data - set, the value (4) has the highest frequency ((5)). After excluding Trevor's data, the value (4) still has the highest frequency ((5)). So the mode remains the same.

Step4: Calculate the original range

The range is the difference between the maximum and minimum values. The original range (R_1=10 - 1=9). After excluding Trevor's data, the new maximum value is (6) and the minimum value is (1), so the new range (R_2=6 - 1=5). So the range decreases.

Answer:

Mean: Decreases Median: Remains the same Mode: Remains the same Range: Decreases