a. The value of a and b are 159 and 636, respectively. Thus, there are 159 animals in the 3-5 kg class interval and 636 animals in the 33-44 kg class interval.
b. An estimate of the lower boundary of the masses of the heaviest 50% of animals would be approximately 9 kg.
How to finding the values of a and b
Let x be the number of animals in the 3-5 kg class interval.
We know that the histogram has four columns of equal height, so there are 4x animals in the 33-44 kg class interval.
We also know that there are a total of 2226 animals treated at the clinic. This can be expressed as:
x + 371 + 1060 + 4x = 2226
Combining like terms
5x = 795
Dividing both sides by 5
x = 159
Therefore, there are 159 animals in the 3-5 kg class interval and 4x = 636 animals in the 33-44 kg class interval.
The table now looks like this:
Mass (kg) No. animals
3-5 159
6-12 371
13-32 1060
33-44 636
To show that a total of 2226 animals were treated
2226 - (159 + 371 + 1060 + 636) = 0
To calculate an estimate of the lower boundary of the masses of the heaviest 50% of these animals, find the class interval that represents the lower boundary of the masses for the heaviest 50% of animals.
The heaviest 50% of animals would correspond to the class interval with the highest masses.
From the given histogram, the class interval with the highest masses is 6-12.
To estimate the lower boundary of this class interval, we take the midpoint of the interval, which is (6 + 12) / 2 = 9 kg.
Therefore, an estimate of the lower boundary of the masses of the heaviest 50% of animals would be approximately 9 kg.