Table of Contents

- 1 Is mean affected by addition?
- 2 What happens to the mean when you add a constant?
- 3 What happens to the mean and the standard deviation of a set of data when the value of each datum is increased by the same amount?
- 4 How do you add value to the mean?
- 5 What will happen to the mean value if all the scores in the distribution increase by 5?
- 6 How does mean affect standard deviation?
- 7 What does the mean tell us about the data?
- 8 Does the mean represent the center of the data?
- 9 How are data points assigned to a cluster?
- 10 How to partition data points in k means clustering?

## Is mean affected by addition?

No matter what value we add to the set, the mean, median, and mode will shift by that amount but the range and the IQR will remain the same.

### What happens to the mean when you add a constant?

Effect of Changing Units If you add a constant to every value, the mean and median increase by the same constant. For example, suppose you have a set of scores with a mean equal to 5 and a median equal to 6. If you add 10 to every score, the new mean will be 5 + 10 = 15; and the new median will be 6 + 10 = 16.

#### What happens to the mean and the standard deviation of a set of data when the value of each datum is increased by the same amount?

As a general rule, the median, mean, and quartiles will be changed by adding a constant to each value. Adding a constant to each value in a data set does not change the distance between values so the standard deviation remains the same.

**How would the mean, median and mode of a data set be affected if each data value were tripled?**

Question: How would the mean, median, and mode of a data set be affected if each data value were tripled? The mean would be tripled, but the median and mode would be unaffected.

**How do extreme values affect the mean?**

Outlier An extreme value in a set of data which is much higher or lower than the other numbers. Outliers affect the mean value of the data but have little effect on the median or mode of a given set of data.

## How do you add value to the mean?

How to Find the Mean

- Count the number of values in your data set.
- Add up all of the values to get the sum.
- Divide the sum by the count.

### What will happen to the mean value if all the scores in the distribution increase by 5?

Adding a new score with a value greater than the mean will increase the mean. For example, if we add a constant of 5 to each score in a distribution, then the mean will increase by 5. If we subtract this constant from all scores, then the mean will decrease by 5.

#### How does mean affect standard deviation?

If every term is doubled, the distance between each term and the mean doubles, BUT also the distance between each term doubles and thus standard deviation increases. If each term is divided by two, the SD decreases. (b) Adding a number to the set such that the number is very close to the mean generally reduces the SD.

**What happens to the mean and standard deviation of the distribution of sample means?**

Thus the mean of the distribution of the means never changes. Thus as the sample size increases, the standard deviation of the means decreases; and as the sample size decreases, the standard deviation of the sample means increases.

**How would the mean median and mode of a data set be affected if each data value were multiplied by a constant C?**

Multiplying each data value by the same constant c results in the mode, median, and mean increasing by a factor of c. Consider a data set of 15 distinct measurements with mean A and median B. The mean would increase while the median would remain the same.

## What does the mean tell us about the data?

The mean is essentially a model of your data set. It is the value that is most common. That is, it is the value that produces the lowest amount of error from all other values in the data set. An important property of the mean is that it includes every value in your data set as part of the calculation.

### Does the mean represent the center of the data?

The “center” of a data set is also a way of describing location. The two most widely used measures of the “center” of the data are the mean (average) and the median. The mean is the most common measure of the center.

#### How are data points assigned to a cluster?

After each data point is assigned to a cluster, reassign the centroid value for each cluster to be the mean value of all the data points within the cluster. This is where the iterative process begins. Follow the same process for initially assigning data points to clusters, this time with new centroid values.

**What happens when you add a data point above the mean?**

If we add a data point that’s above the mean, or take away a data point that’s below the mean, then the mean will increase. If take away a data point that’s above the mean, or add a data point that’s below the mean, the mean will decrease.

**How to find the mean of a data set?**

Mean: Add all the numbers together and divide the sum by the number of data points in the data set. Median: Arrange all the data points from small to large and choose the number that is physically in the middle. If there is an even number of data points, then choose the two numbers in the (physical) middle and find the mean of the two numbers.

## How to partition data points in k means clustering?

K-means clustering is a simple method for partitioning $n$ data points in $k$ groups, or clusters. Essentially, the process goes as follows: Select $k$ centroids. These will be the center point for each segment. Assign data points to nearest centroid. Reassign centroid value to be the calculated mean value for each cluster.