Given a histogram. How would I find out how far the mean was from the median?
To find out how far the mean is from the median in a histogram, you need to follow these steps:
1. Calculate the mean: The mean is the average of all the values in the histogram. To calculate the mean, multiply each data value by its frequency (the number of times it appears), sum the products, and divide by the total number of data points.
2. Calculate the median: The median is the middle value in the ordered set of data. To find the median, arrange the data points in ascending order and identify the middle value.
3. Subtract the median from the mean: Once you have the mean and median values, subtract the median from the mean. The resulting value will indicate how far the mean is from the median.
Here's an example using a simplified histogram:
Data: 2, 3, 3, 4, 5, 5, 5, 6, 6, 7, 11
Frequencies: 1, 2, 3, 1, 3, 2, 1
Step 1: Calculate the mean:
(2*1 + 3*2 + 4*1 + 5*3 + 6*2 + 7*1 + 11*1) / (1 + 2 + 1 + 3 + 2 + 1 + 1) = 56 / 11 ≈ 5.09
Step 2: Calculate the median:
After arranging the data points in ascending order: 2, 3, 3, 4, 5, 5, 5, 6, 6, 7, 11
The median is the middle value, which is 5 in this case.
Step 3: Calculate the difference:
Mean - Median = 5.09 - 5 = 0.09
So, the mean is 0.09 units away from the median.
Note that in a histogram, you may have grouped or binned data, so you will need to adjust the steps accordingly.