THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A recent survey asked respondents about their monthly purchases of raffle tickets.The monthly expenditures,in dollars,of ten people who play the raffle are 23,15,11,20,28,35,13,10,20,and 24. -Which of the following statements is not true? A)The 75^th percentile is equal to 23.5. B)The median is equal to the mode. C)The mean is 19.9. D)The distribution is approximately symmetric.

Question

Quizplus · Accepted Answer

The 75th percentile is the value that is greater than or equal to 75% of the data set. When the data set is arranged in ascending order, the 75th percentile is the value at the index of (0.75(n+1)). In this case, n=10, so the index is at (0.75(10+1)) = 8.25. The 8th value in the ordered data set is 24, and the 9th value is 28. To find the 75th percentile, we can use linear interpolation to estimate the value between these two values:

75th percentile = 24 + (0.25)*(28-24) = 25

Therefore, statement A is not true as the 75th percentile is not equal to 23.5.

B) The median is equal to the mode. This statement may or may not be true as we need to calculate the median and the mode to confirm.

C) The mean is 19.9. This statement can be confirmed by finding the sum of the data set and dividing by the number of observations:

(23+15+11+20+28+35+13+10+20+24)/10 = 199/10 = 19.9

D) The distribution is approximately symmetric. This can be confirmed by creating a histogram or a boxplot to visualize the distribution, or by calculating the skewness. However, based on the information given in the question, we cannot confirm or refute this statement.