In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying numbers of mangoes. The following was the distribution of mangoes according to the number of boxes.

• Number of mangoes: 50 - 52, 53 - 55, 56 - 58, 59 - 61, 62 - 64
• Number of boxes: 15, 110, 135, 115, 25

Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?

To find the mean number of mangoes kept in a packing box, we can use the weighted average method. This approach is suitable here because we have different quantities of mangoes in each range and their corresponding number of boxes.

Step-by-Step Calculation

1. Calculate the Midpoint for Each Range

First, we need to find the midpoint of each range of mangoes:

• 50 - 52: Midpoint = (50 + 52) / 2 = 51
• 53 - 55: Midpoint = (53 + 55) / 2 = 54
• 56 - 58: Midpoint = (56 + 58) / 2 = 57
• 59 - 61: Midpoint = (59 + 61) / 2 = 60
• 62 - 64: Midpoint = (62 + 64) / 2 = 63

2. Multiply Each Midpoint by the Number of Boxes

Next, we multiply each midpoint by the number of boxes:

• 51 * 15 = 765
• 54 * 110 = 5940
• 57 * 135 = 7695
• 60 * 115 = 6900
• 63 * 25 = 1575

3. Sum the Products and the Total Number of Boxes

Now, we add up all the products and the total number of boxes:

• Total of products = 765 + 5940 + 7695 + 6900 + 1575 = 22875
• Total number of boxes = 15 + 110 + 135 + 115 + 25 = 400

4. Calculate the Mean

Finally, we find the mean by dividing the total products by the total number of boxes:

Mean = Total Products / Total Boxes = 22875 / 400 = 57.1875

Final Result

The mean number of mangoes kept in a packing box is approximately 57.19.