Median of Plant A: 5.8 Mode of Plant A: 5.4 Range of Plant A: 1.2 Mean of Plant B: 5.6 Median of Plant B: 5.5 Mode of Plant B: None Range of Plant B: 2.9
B
b See solution.
C
c See solution.
Practice makes perfect
a We are asked to calculate the measures of central tendency and the range of data collected from two manufacturing plants. We will do this one plant at a time.
Plant A
We will begin by writing the values of the data set from least to greatest.
5.2, 5.4, 5.4, 5.7, 5.8, 6.1, 6.3, 6.4
We can see that there are 8 values in the data set. To calculate the mean of the data, we need to add every value and divide the sum by 8. Let's do it!
Mean: 5.2+ 5.4+ 5.4+ 5.7+ 5.8+ 6.1+ 6.3+ 6.4/8
⇓
Mean: 5.7875
Therefore, the mean of the set is about 5.8. Now, since we have 8 values in the set, we need to calculate the average of the values in the middle of the set to find the median of the data. Let's look for the values in the middle of the data.
5.2, 5.4, 5.4, 5.7, 5.8, 6.1, 6.3, 6.4
Now calculate the average of these values to find the median of the data.
Median: 5.7+ 5.8/2 = 5.75
The median of the set is about 5.8. To find the mode of the data we need to look for the number with most repetitions. Let's do it!
5.2, 5.4, 5.4, 5.7, 5.8, 6.1, 6.3, 6.4
Since it is the only value repeated in the set, the mode is 5.4. Finally, to find the range of the set we need to subtract the least value from the greatest value.
Range: 6.4 - 5.2 = 1.2
Plant B
Let's write the values of the data set from least to greatest.
4.3, 4.5, 4.9, 5.2, 5.7, 6.3, 6.4, 7.2
We can see that there are 8 values in the data set. To calculate the mean of the data we need to add every value and divide the sum by 8. Let's do it!
Mean: 4.3+ 4.5+ 4.9+ 5.2+ 5.7+ 6.3+ 6.4+ 7.2/8
⇓
Mean: 5.5625
The mean of the set is about 5.6. Now, since we have 8 values in the set we need to calculate the average of the values on the middle of the set to find the median of the data. Let's look for the values in the middle of the data.
4.3, 4.5, 4.9, 5.2, 5.7, 6.3, 6.4, 7.2
Now let's calculate the average of these values to find the median of the data.
Median: 5.2+ 5.7/2 = 5.45
The median of the set is about 5.5. To find the mode of the data we need to look for the value with the most repetitions in the data. Let's do it!
4.3, 4.5, 4.9, 5.2, 5.7, 6.3, 6.4, 7.2
We can see that there are no values repeated in the set. Therefore, the data has no mode. Finally, to find the range of the set we need to subtract the least value from the greatest value.
Range: 7.2 - 4.2 = 2.9
b Since there are no outliers in the set, the mean is the best measure to describe the data from the plant A.
Mean of Plant A: 5.8
Since 7.2 can be an outlier, both the median and the mean are good measures to describe the data from Plant B.
Mean of Plant B: 5.6
Median of Plant B: 5.5
These measures are also very close.
c We can see that in the plot the greater values are at the bottom. Therefore, the data set that has more values concentrated at the bottom has the greater mean. In this case it is Plant A.
