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The following data represents the number of automobiles arriving at a toll booth during 20 intervals, each of ten-minute duration. Compute the mean, median, mode, first quartile, and third quartile for data... (please see attachment for remainder of questions).

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The following data represents the number of automobiles arriving at a toll booth during 20 intervals, each of ten-minute duration. The solution computes the mean, median, mode, first quartile, and third quartile for data.

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Ch 3
Ex. 11

The following data represents the number of automobiles arriving at a toll booth during 20 intervals, each of ten-minute duration. Compute the mean, median, mode, first quartile, and third quartile for data.

26 26 58 24 22 22 15 33 19 27
21 18 16 20 34 24 27 30 31 33

Solution. Mean=[26+26+58+...+30+31+33]/20=26.3
Median=25
How to get it? You can re-order the data in increasing order:
15,16, 18, 19, 20, 21, 22, 22, 24, 24 , 26,26, 27, 27, 30, 31, 33,33, 34, 58.
Then you can find two numbers in the middle(since the total is 20 which is even, if the total is odd, then there is only one number in the middle) which are 24 and 26. So, the average is 25. So the Median is 25.
Mode=26
First quartile=(20+21)/2=20.5
The first quartile is the median of the lower half of the data, that is, the median of
15,16, 18, 19, 20, 21, 22, 22, 24, 24, is 20.5;

Third quartile=(30+31)/2=30.5
The third quartile is the median of the upper half of the data, ...

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• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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