The completed grouped frequency table is
Temperature Frequency
4 ≤ t < 6 5
6 ≤ t < 8 2
8 ≤ t < 12 2
The estimate of the mean is 6.6
How to complete the grouped frequency table
From the question, we have the following parameters that can be used in our computation:
The histogram
Reading from the histogram, we have
- The frequency of the group 4 ≤ t < 6 is 5
- The frequency of the group 6 ≤ t < 8 is 2
- The frequency of the group 8 ≤ t < 12 is 2
So, we have that
x = 5, y = 2 and z = 2
For the mean, we start by calculating the midpoint of the classes
So, we have
4 ≤ t < 6: Midpoint = 1/2(4 + 6) = 5
6 ≤ t < 8: Midpoint = 1/2(6 + 8) = 7
8 ≤ t < 12: Midpoint = 1/2(8 + 12) = 10
The mean is then calculated as
Mean = ∑fx/∑f
So, we have
Mean = (5 * 5 + 2 * 7 + 2 * 10)/(5 + 2 + 2)
Evaluate
Mean = 6.6
Hence, the mean is 6.6