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### Course: High school statistics>Unit 1

Lesson 3: Mean and median in data displays

# Choosing the "best" measure of center

Mean and median both try to measure the "central tendency" in a data set. The goal of each is to get an idea of a "typical" value in the data set. The mean is commonly used, but sometimes the median is preferred.

### Part 1: The mean

A golf team's $6$ members had the scores below in their most recent tournament:
$70,\phantom{\rule{0.167em}{0ex}}72,\phantom{\rule{0.167em}{0ex}}74,\phantom{\rule{0.167em}{0ex}}76,\phantom{\rule{0.167em}{0ex}}80,\phantom{\rule{0.167em}{0ex}}114$
problem a
Calculate the mean score.
mean =

problem b
What is a correct interpretation of the mean score?

### Part 2: The median

problem a
Find the median score.
As a reminder, here are the scores: $70,\phantom{\rule{0.167em}{0ex}}72,\phantom{\rule{0.167em}{0ex}}74,\phantom{\rule{0.167em}{0ex}}76,\phantom{\rule{0.167em}{0ex}}80,\phantom{\rule{0.167em}{0ex}}114$
median =

problem b
What is a correct interpretation of the median score?

### Part 3: The "best" measure of center

Which measure best describes the scores of the team?
As a reminder, here are the scores: $70,\phantom{\rule{0.167em}{0ex}}72,\phantom{\rule{0.167em}{0ex}}74,\phantom{\rule{0.167em}{0ex}}76,\phantom{\rule{0.167em}{0ex}}80,\phantom{\rule{0.167em}{0ex}}114$
The
best describes the scores of the team, because the
is higher than almost all of the scores in the data set.

## Want to join the conversation?

• What if there would be more same scores, lets say : 70, 70, 70, 75 , 80 , 90, 120.
The mean would be best to describe?
• the mean is so high bc of the outliar
• How can you tell what the median is if the is two numbers in the middle?
• You would have to take the average of the two numbers in the middle (add them and then divide by 2).
• When there is an outlier, which measure of center is better to choose (mean or median)
• here's another solution
discard two (or more) extreme data points like the smallest and the largest
and get the mean of the left

in many practical cases, this works better than simple mean or median methods
• Please can someone help me with this problem it says:
A set of data has 10values no two of which are the same if the smallest value is removed from the set . Which of these statements must be true.
- the range of the first data set is greater than the range of the second data set.
- the mode of the first data set is greater than the mode of the second data set.
-the medians of the two data sets are the same .
- the mean of the first data set is greater than the mean of the second data set.
• your original set could be: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
your new set is now: 2, 3, 4, 5, 6, 7, 8, 9, 10

-the first data set's range is greater (9>8).
-neither set has a mode
-second data set's median is greater (6>5.5)
-2nd data mean is greater: (2+3+4+5+6+7+8+9+10)/9=6
(1+2+3+4+5+6+7+8+9+10)/10=5.5
• How do you determine the mean and mode when the data set of numbers is too big to visualize individually?
• You use computers a lot, basically! This is where software such as Excel, and programming languages such as R and Python come in handy.
• When you find the median and its 2 numbers like 75 and 68 how do you find the middle? Would you put them from least to greatest, add then divide by 2?
• If the median falls between two numbers, simply add those two numbers, then divide by 2. In the case you mentioned, 71.5 is halfway between 75 an 68.