Homework on Intro to Statistics

Notes on Measures of Center Name______

The mean of a data set can be determined by dividing the sum of the data values by the total number of data values. It is the same as the average.

Suppose Carrie wants the mean of her four test scores: {80, 90, 72, 68}.

In order to find the mean, first add all of the numbers together: 80 + 90 + 72 + 68 = 310.

Next, divide this sum by the number of data values in the set. Since there are four values, calculate 310 4 = 77.5. ASK YOUR TEACHER WHAT NOT TO DO!!!

77.5 is the mean of the test scores. Note that it is possible for the mean to be a decimal value. ------In trying to form its monthly budget, the James' family looked at its monthly Georgia Power bills for the last twelve months. Here are the amounts found on those bills:

$70, $75, $88, $110, $115, $110, $123, $144, $117, $90, $99, $71

If the family chooses to use the mean for its budget, what would be the amount used? Round to the nearest whole number of dollars. ------The mode of a data set is the most frequently occurring value in the data set.

In the data set {5, 6, 7, 7, 7, 10}, '7' is the mode because it occurs more often than any other data value.

If two or more data values occur "equally the most", then each of those values is part of the mode.

For example, in the data set {0, 1, 1, 3, 3}, the numbers '1' and '3' both occur the most of any of the numbers in the set. Therefore, "1 and 3" would be deemed the mode of this set.

Finally, if all data values occur one time, then there is "no mode". ------If the James' family chooses to use the mode for the budgeted amount for the power bill, what would be the amount used? ------The median of a data set is the middle value of the data set once it has been ordered from least to greatest, or vice-versa.

For example, in the data set {3, 1, 8, 10, 6}, one should put the numbers in order to find the median. So, after rearranging the set to read {1, 3, 6, 8, 10}, it is easy to see that '6' is the middle value. Hence, '6' is the median.

If there are an even number of data values in the set, then the median is determined by averaging the two middle entries.

In the data set {1, 8, 6, 3}, there are an even number of data values. First, place the values in order {1, 3, 6, 8}. As you can see, the two "middle" values are '3' and '6'. After averaging '3' and '6', one can obtain the median. The median is '4.5'. ------If the James' family chooses to use the median, what would be the amount used?

$70, $75, $88, $110, $115, $110, $123, $144, $117, $90, $99, $71

------VERY IMPORTANT - The mean, median, and mode are called measures of center, because they are all different ways of locating the approximate center of the data set. ------The following data set represents the number of wins by college football teams in the Southeastern Conference in 2009: {2, 5, 7, 7, 7, 8, 8, 8, 9, 9, 13, 14}.

What is the mean number of wins for a team in the SEC?

What is the mode number of wins for a team in the SEC?

What is the median number of wins for a team in the SEC? ------When comparing two data sets, the three measures of center (mean, median, and mode) can be used to answer various questions. For example, suppose one wants to know, "Who is the best Math student in the class." One way to determine the best is to compare the means of all of the students. The student with the highest mean could be considered the best student.

Fans like to compare the SEC (from above) to another group known as the ACC in order to determine which conference is better.

Here are the twelve teams in the ACC and their number of wins:

Team Wins Team Wins Clemson 9 Georgia Tech 11 Boston College 8 Virginia Tech 10 Florida State 7 Miami 9 Wake Forest 5 North Carolina 8 N.C. State 5 Duke 5 Maryland 2 Virginia 3

Compute the mean number of wins for the ACC. By comparing the mean number of wins in the SEC and in the ACC, which conference is the better conference?

Now, compare the medians. Which conference is the better conference based on the medians?

Finally, compare the modes of the two data sets. Which conference is the better conference based on the modes.

Based on these findings, make a statement about which conference was better in 2009? Homework on Measures of Center Name______

1. Consider the following set of numbers: {1, 9, 11, 10, 5, 5, 3, 9}.

a)What is the mean?

b)What is the median?

c)What is the mode? ------2. Here are the stock prices for Holbrook Group over the last nine days:

$45, $46, $45, $48, $51, $53, $55, $54, $44

a)What is the median?

b)What is the mode?

c)What is the mean? ------3. Here are the final scores for Phil Mickelson and Tiger Woods in the past six Masters' tournaments from 2005 to 2010:

Mickelson: {299, 281, 285, 279, 283, 272} Woods: {291, 284, 276, 290, 290, 277}

A)Find the median score for both golfers. Based on the median, who has been the better golfer in the last six tournaments if a lower score is desired in golf?

B)Find the mean score for both golfers. Based on the mean scores, who have been the better golfer in the last six tournaments?

C)Why do you think it would not be beneficial to compare the modes of the golfers?

------4. Suppose Caroline has grades of 98, 60, and 71 on three tests. If there is only one test remaining, what must her grade be on the final test in order to have a mean test score of exactly 80?

------5. Compose a set of seven numbers with a mode of 25 and a median of 10.

------6. Compose a set of four numbers that has a median of 12 and a mode of 1.