Question

20 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 shows 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 grans) Frequency (i) (ii (ii) (iv) 80-1O0 20 100-120 60 120-1-40 140-16O 70 How many apples are in the range 140-160 mass? What is the mean mass of the apples? What is the modal mass of the apples? What is the upper limit of the median class? 160-1SO 60​

Answer 1

Explanation:

In the given table, the range 140-160 mass has a frequency of 70. This means that there are 70 apples in that range.

To find the mean mass of the apples, we need to calculate the average. We can do this by adding up the products of the midpoints and frequencies of each range, and then dividing by the total number of apples.

Midpoint of 80-100 range = (80 + 100)/2 = 90

Midpoint of 100-120 range = (100 + 120)/2 = 110

Midpoint of 120-140 range = (120 + 140)/2 = 130

Midpoint of 140-160 range = (140 + 160)/2 = 150

Midpoint of 160-180 range = (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)

= (1800 + 6600 + 18200 + 10500 + 10200) / 350

= 56300 / 350

= 160.857 grams (rounded to 3 decimal places)

The modal mass of the apples is the mass value that occurs most frequently. In the given table, the range 120-140 has the highest frequency of 140. Therefore, the modal mass of the apples is in the range 120-140 grams.

The upper limit of the median class can be found by calculating the cumulative frequency. The median class is the class where the cumulative frequency is equal to or greater than half of the total number of apples.

Cumulative frequency of the first class: 20

Cumulative frequency of the second class: 20 + 60 = 80

Cumulative frequency of the third class: 80 + 140 = 220

Since the cumulative frequency of the third class is greater than half of the total number of apples, the upper limit of the median class is 140 grams.

Please let me know if I am wrong.