Multiple choice

If the mean of the following frequency distribution is 2.7, and total of frequencies is 20, then find x and y. | Data | 1 | 2 | 3 | 4 | 5 | | --- | --- | --- | --- | --- | --- | | Frequency | 5 | x | 4 | 3 | y |

  1. 7, 1

  2. 6, 2

  3. 5, 3

  4. 4, 4
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total frequency = 5 + x + 4 + 3 + y = 20, so x + y = 8. Mean = (1*5 + 2*x + 3*4 + 4*3 + 5*y) / 20 = 2.7. 5 + 2x + 12 + 12 + 5y = 54. 2x + 5y = 25. Solving the system: x = 8 - y, so 2(8-y) + 5y = 25 => 16 + 3y = 25 => 3y = 9 => y = 3. Then x = 5.

AI explanation

Using the total frequency gives the equation 5 + x + 4 + 3 + y = 20, which simplifies to x + y = 8. Using the mean formula gives (5 + 2x + 12 + 12 + 5y)/20 = 2.7, which simplifies to 2x + 5y = 25. Multiplying the first equation by 2 gives 2x + 2y = 16, and subtracting this from the second equation yields 3y = 9, so y = 3; substituting back gives x = 5.

Keep practicing — related questions