i need to find from the following data
the outlier and how the outlier affects the mean.
find also the
mean median mode
here are the numbers:
156
145
162
215
148
163
here is what i got:
outlier; 215
with the outlier the mean is: 164.8
with out the outlier mean is: 154.8
mean is: 164.8
median : 159
mode: there is no number that is listed 2 times so no mode
you have it correct.
To find the outlier and understand its effect on the mean, you can follow these steps:
Step 1: Sort the data in ascending order:
145, 148, 156, 162, 163, 215
Step 2: Identify the outlier:
Looking at the data, we can see that 215 is the outlier as it is significantly larger than the other numbers.
Step 3: Calculate the mean with and without the outlier:
With the outlier included, the sum of all the numbers is 145 + 148 + 156 + 162 + 163 + 215 = 989. Divide this sum by the total number of data points (6) to get the mean: 989/6 = 164.8.
To get the mean without the outlier, exclude 215 from the sum: 145 + 148 + 156 + 162 + 163 = 774. Divide this sum by the revised total number of data points (5) to get the mean: 774/5 = 154.8.
So, with the outlier included, the mean is 164.8, and without the outlier, the mean is 154.8.
Now, let's find the median and mode:
Median: To find the median, arrange the data in ascending order (already done in step 1). Since there is an odd number of data points, the median is the middle value, which is 162.
Mode: The mode represents the value(s) that occur most frequently. In this dataset, there is no number that is repeated, so there is no mode.
Therefore, the results are as follows:
Outlier: 215
Mean (with outlier): 164.8
Mean (without outlier): 154.8
Median: 162
Mode: None (no mode)