Given Data:
The weight (in kg) of 45 students of a class is given in the following distribution table.

Weight (in kg) | Number of Students
---------------|------------------
40 | 3
42 | 5
44 | 8
46 | 12
48 | 9
50 | 5
52 | 3

Objective:
To determine the value of weight x, such that the number of students having weight less than x kg is the same as the number of students having weight more than x kg.

Approach:
To find the value of weight x, we will follow the following steps:

1. Calculate the cumulative frequency for each weight category.
2. Identify the weight category where the cumulative frequency is closest to half of the total number of students.
3. Determine the lower and upper bounds of the weight category identified in step 2.
4. Use linear interpolation to find the weight x at which the number of students having weight less than x kg is the same as the number of students having weight more than x kg.

Step 1: Calculate Cumulative Frequency:
To calculate the cumulative frequency, we add up the number of students for each weight category.

Weight (in kg) | Number of Students | Cumulative Frequency
---------------|-------------------|---------------------
40 | 3 | 3
42 | 5 | 8
44 | 8 | 16
46 | 12 | 28
48 | 9 | 37
50 | 5 | 42
52 | 3 | 45

Step 2: Identify the Closest Cumulative Frequency:
We observe that the cumulative frequency closest to half of the total number of students (45/2 = 22.5) is 28. This corresponds to the weight category of 46 kg.

Step 3: Determine Lower and Upper Bounds:
The lower bound of the weight category is 46 kg, and the upper bound is 48 kg.

Step 4: Use Linear Interpolation:
To find the weight x at which the number of students having weight less than x kg is the same as the number of students having weight more than x kg, we can use linear interpolation.

Linear interpolation formula: x = L + (F1 - F2) * (U - L) / (F1 - F2)

Where:
x = weight x
L = lower bound
U = upper bound
F1 = cumulative frequency of lower bound
F2 = cumulative frequency of upper bound

In this case, L = 46 kg, U = 48 kg, F1 = 28, and F2 = 37.

Substituting the values into the formula: x = 46 + (28 - 22.5) * (48 - 46) / (28 - 22.5)

Simplifying the equation, we get: x = 46 + 5.5 * 2 / 5.5 = 46 + 2 = 48

Result:
The value of weight x, at which the number of students having weight less than x kg is the same as the number of students having weight

Where is the distribution table??