a Start by finding the outlier. Then calculate the mean, median, and mode for the given values with and without the outlier.
B
b Does a younger panda bear weigh the same as an adult panda bear?
A
aOutlier: 62 kilograms
Mean: The outlier decreases the mean by about 42.5 kilograms. Median: The outlier increases the median by 3 kilograms.
Mode: The outlier does not affect the mode.
B
bSample Answer: It represents the mass of a baby polar bear.
Practice makes perfect
a The following table represents the mass of eight polar bears.
Masses (Kilograms)
455
262
471
358
364
553
62
351
We are asked to find the outlier of the given data set. An outlier is a data value that is much greater than or much less than the other values in a data set. In this case, 62 is much less than the other masses. Therefore, it is the outlier. To find out how this value affects the measures of center, let's analyze each measure one at a time.
Mean
The mean of a numerical data set is the sum of the data divided by the number of data values. Let's calculate the mean without removing the outlier. Since we have 8 data values, the mean will be the sum of the data values divided by 8.
Now, we need to remove the outlier from the given values.
455, 364, 262, 553, 471, 62, 358, 351
⇓
455, 364, 262, 553, 471, 358, 351
Proceeding in the same way, we can calculate the mean for the values without the outlier. In this case, we have 7 data values.
We can see that the mean of the values with the outlier is less than the mean of the values without the outlier. Let's find the difference of these means.
402-359.5=42.5
Therefore, the outlier decreases the mean by about 42.5 kilograms.
Median
The median of a numerical data set is the middle number when the values are written in numerical order. If the data set has an even number of values, the mean of the two middle values will be the median. Let's first find the median without removing the outlier. To do so, let's write the given values in numerical order.
62, 262, 352, 358, 364, 455, 471, 553
Since we have an even number of data values, we have to calculate the mean of the two middle values.
Median&=358+ 364/2
&⇓
Median&=361
Now, let's take a look at the given values without the outlier.
262, 352, 358, 364, 455, 471, 553
In this case the median is 364 kilograms. Comparing the medians, we can see that the median with the outlier is less. Let's calculate the difference of these medians.
364-361=3
Therefore, the outlier decreases the median by 3 kilograms.
Mode
The mode of a data set is the value or values that occur most often. Let's take a look at the values with and without the outlier.
With Outlier: & 62, 262, 352, 58,
&364, 455, 471, 553 [0.5em]
Without Outlier:&262, 352, 58, 364,
&455, 471, 553
Note that for both data sets all of the values occur once. There is no mode in each data set. Therefore, the outlier does not affect the mode.
b One possible explanation for the outlier could be that it represents the mass of a baby polar bear. Therefore, it weighs less. Please note that there are many possible explanations. Here we are only considering one possibility.
