Question

Apples are most widely planted and are commercially the most important fruit crop in Jammu and Kashmir. The cultivation of apple crop in Jammu and Kashmir show particular interest for a number of reasons. In terms of both area and production apple is very beneficial fruit crop. This provides a major source of income and employment in Jammu and Kashmir. Horticultural department has tasked their statistical officer to create a model for farmers to be able to predict their produce output based on various factors. A box containing 250 apples was opened and each apple was weighed. The distribution of the masses of the apples is given in the following table: Mass (in grams) Frequency (i) (iii) (iv) 80-100 20 100-120 60 120-140 140-160 70 How many apples are in the range 140-160 mass? What is the mean mass of the apples? What is the upper limit of the median class? What is the modal mass of the apples? 160-180 60​

Answer 1

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).