I need to find the measures of spread and center for each data set in a problem I am doing. How do I do that?

Also, is the center the mean(average)? Or the median?

In a normal distribution, the mean, median and mode have essentially the same value. All are measures of central tendency.

Range and standard deviation are measures of variability or spread.

To find the measures of spread and center for a data set, you can follow these steps:

1. Measure of Spread: Start by calculating the range of the data set, which is the difference between the maximum and minimum values.

Range = Maximum Value - Minimum Value

This measure tells you the spread of the data over its entire range.

2. Next, you can find the interquartile range (IQR), which gives you a measure of spread that is less affected by outliers. To calculate the IQR:

a. Sort the data set in ascending order.
b. Find the median, which is the middle value of the data. If the data set has an odd number of values, the median is the single middle value. If the data set has an even number of values, the median is the average of the two middle values.
c. Split the data into two halves: the lower half and the upper half. Ignore the median when splitting.
d. Find the median of the lower half, which is called the first quartile (Q1).
e. Find the median of the upper half, which is called the third quartile (Q3).
f. Calculate the IQR by subtracting Q1 from Q3.

IQR = Q3 - Q1

The IQR provides a measure of spread that focuses on the middle 50% of the data.

3. Measure of Center: The center of a data set can be represented by either the mean (average) or the median.

- Mean: To calculate the mean, add up all the values in the data set and divide the sum by the total number of values.

Mean = Sum of all values / Number of values

The mean represents the average value of the data set.

- Median: To find the median, sort the data set in ascending order and find the middle value. If the data set consists of an odd number of values, the median is the single middle value. If the data set consists of an even number of values, the median is the average of the two middle values.

The median represents the value that separates the higher half from the lower half of the data set.

In summary, the measures of spread include the range and interquartile range, while the measures of center can be represented by the mean (average) or the median.