Expert: Sherry Wallin - 6/12/2010

Question
Dear Sherry,

Please, explain in brief so that I can understand how come the answers are 117.5 / 6 / 10.25, respectively.

For the class 110 – 117 of a given frequency distribution, what is the upper class boundary?  
Answer: 117.5

For the classes 27 – 32, 33 – 38, 39 – 44, what is the class width? Answer: 6

A motorist recorded the number of gallons of gasoline he used for 8 weeks. The results are as follows: 11, 11, 11, 10, 9, 11, 9, and 10. The mean number of gallons used would be:
Answer: 10.25

Answer
Yankgun~
    For number one without seeing the distribution I can't tell you why the upper class boundary is 117.5. Maybe the distribution is in increments of .5 or else there is a typo in the question. As for number two the class width is just how many values are in the range. For example count the elements in the first class: 27, 28, 29, 30, 31, 32. See there are six elements in each of those classes. There is an easier way to know this instead of counting the elements. And that is when you are including the ends as in 27 and 32 always add one to the upper end of the range and subtract the lower end of the range 33-27 = 6. And finally for number three, just add the numbers, count how many you added and divide it into the sum of the numbers:
I see four 11's = 44 and I see two 10's which is 20, and I see two 9's which is 18 so
44 + 20 + 18 = 82 and there were 8 numbers so 82/8 = 10.25 which is your mean.

or if you prefer 11 + 11 + 11 + 10 + 9 + 11 + 9 + 10 = 82 and 82/8 = 10 2/8 = 10 1/4 = 10.25

Math Prof