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b. do trucks or convertibles have a greater range of sales over the 8 -…

Question

b. do trucks or convertibles have a greater range of sales over the 8 - week period? weekly car sales at automart (in thousands of dollars) trucks: 350, 125, 415, 370, 560, 280, 265, 430; convertibles: 640, 720, 600, 640, 810, 755, 780, 660. the following data show the ages of 20 students graduating from college. 22, 22, 23, 22, 25, 26, 22, 21, 22, 26, 64, 22, 23, 24, 22, 25, 22, 22, 24, 59. c. identify any outliers in the data set. d. describe how any outliers affect the measures of central tendency.

Explanation:

Response
Part b

Step1: Find range for Trucks

Range = Max - Min. For Trucks: Max = 560, Min = 125. So range = \( 560 - 125 = 435 \).

Step2: Find range for Convertibles

For Convertibles: Max = 810, Min = 600. So range = \( 810 - 600 = 210 \).

Step3: Compare ranges

435 > 210, so Trucks have greater range.

Brief Explanations

To identify outliers, we can use the interquartile range (IQR) method. First, order the data: 21, 22, 22, 22, 22, 22, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 59, 64. Wait, original data: 21, 22 (8 times), 23 (2), 24 (2), 25 (2), 26 (2), 59, 64. Wait, n = 20. Q1 (25th percentile): position = \( 0.25\times20 = 5 \), so Q1 is average of 5th and 6th terms (both 22, so Q1 = 22). Q3 (75th percentile): position = \( 0.75\times20 = 15 \), 15th term is 26, 16th term is 26, so Q3 = 26. IQR = Q3 - Q1 = \( 26 - 22 = 4 \). Lower fence: \( Q1 - 1.5\times IQR = 22 - 6 = 16 \). Upper fence: \( Q3 + 1.5\times IQR = 26 + 6 = 32 \). Values 59 and 64 are above 32, so they are outliers.

Brief Explanations
  • Mean: Outliers (59, 64) are much larger than most data. Mean is sum of all values divided by n. Including outliers increases the sum, so mean is pulled up (becomes larger than without outliers).
  • Median: Median is the middle value (for n=20, average of 10th and 11th terms). Most data is around 22 - 26, and outliers are at the end. The middle values are still in the main cluster, so median is less affected.
  • Mode: Mode is the most frequent value (22). Outliers don't affect the frequency of 22, so mode remains the same.

Answer:

Trucks

Part c