Height(cm) 160 161 162 163 164 165 No. of players 4 6 3 7 8 9 the table shows the height of 37 players of a…

Step 1: Understand the question We need the mean height from a frequency table: Mean = Σfx ÷ Σf.

Step 2: Check the total frequency 4 + 6 + 3 + 7 + 8 + 9 = 37 ✓. This matches the 37 players stated.

Step 3: Compute Σfx It is easier to use deviations from 160:

• 160: 4 × 0 = 0
• 161: 6 × 1 = 6
• 162: 3 × 2 = 6
• 163: 7 × 3 = 21
• 164: 8 × 4 = 32
• 165: 9 × 5 = 45

Sum of deviations = 0 + 6 + 6 + 21 + 32 + 45 = 110

Step 4: Find the mean Mean = 160 + 110/37 = 160 + 2.973 = 162.973 ≈ 163.0 (to 1 d.p.)

Step 5: Choose the option The mean is 163.0, which is option A.

Exam tip: For a frequency table with consecutive values, subtract a convenient assumed mean (such as the smallest value) to keep the numbers small. Then add it back at the end. Also always check that Σf matches the total given in the question.