Assume the assumed mean\(a = 40\) | Marks (\(x_i\)) | No. of Students (\(f_i\)) | \(f_i x_i\) | \(d_i = x_i - a = x_i - 40\) | \(f_i d_i\) | |------------------|---------------------------|-------------|------------------------------|--------------| | 30 | 4 | 120 | -10 | -40 | | 33 | 7 | 231 | -7 | -49 | | 35 | 10 | 350 | -5 | -50 | | 40 = \(a\) | 15 | 600 | 0 | 0 | | 43 | 8 | 344 | 3 | 24 | | 45 | 5 | 225 | 5 | 25 | | 48 | 3 | 144 | 8 | 24 | | **Total** | \(\sum f_i = 52\) | \(\sum f_i x_i = 2014\) | | \(\sum f_i d_i = -66\) | ### ???? Direct Method: \[ \text{Mean} = \frac{\sum f_i x_i}{\sum f_i} = \frac{2014}{52} \approx 38.73 \] ### ???? Assumed Mean Method: \[ \text{Mean} = a + \frac{\sum f_i d_i}{\sum f_i} = 40 + \frac{-66}{52} = 40 - 1.27 \approx 38.73 \] Therefore, the average marks of the students is approximately 38.73 using both methods.