Answer:
Step-by-step explanation: Based on the given table, let's answer the questions:
How many apples are in the range 140-160 mass?
The frequency for the mass range 140-160 is 70. Therefore, there are 70 apples in the range 140-160 mass.
What is the mean mass of the apples?
To calculate the mean mass, we need to find the midpoint of each mass range and multiply it by its corresponding frequency. Then we sum up these values and divide by the total frequency.
Midpoint of 80-100: (80 + 100) / 2 = 90
Midpoint of 100-120: (100 + 120) / 2 = 110
Midpoint of 120-140: (120 + 140) / 2 = 130
Midpoint of 140-160: (140 + 160) / 2 = 150
Midpoint of 160-180: (160 + 180) / 2 = 170
Now, let's calculate the mean mass:
Mean mass = (90 * 20 + 110 * 60 + 130 * 140 + 150 * 70 + 170 * 60) / (20 + 60 + 140 + 70 + 60)
Mean mass = 130.21 grams (approx.)
Therefore, the mean mass of the apples is approximately 130.21 grams.
What is the upper limit of the median class?
The median class is the class that contains the median value. To determine the upper limit of the median class, we need to find the cumulative frequency of the previous classes until we reach the median class.
Cumulative frequency for 80-100: 20
Cumulative frequency for 100-120: 20 + 60 = 80
Cumulative frequency for 120-140: 80 + 140 = 220
Since the cumulative frequency of the median class is greater than half of the total frequency (which is 250/2 = 125), the median class is the 120-140 mass range.
The upper limit of the median class is 140 grams.
What is the modal mass of the apples?
The modal class is the class with the highest frequency. In this case, the 120-140 mass range has a frequency of 140, which is the highest among all the ranges. Therefore, the modal mass of the apples is within the 120-140 grams range.
Please note that the given frequency table seems to be incomplete as there is no entry for (ii).