A mean is an arithmetic average of a set of observations. The amount that Jack has to earn in tips on Sunday if he wants to average $19 a day is $25.
<h3>What is Mean?</h3>
A mean is an arithmetic average of a set of observations. it is given by the formula,
![\rm Mean=\dfrac{\text{Sum of all obervation}}{\text{Number of observation}}](https://tex.z-dn.net/?f=%5Crm%20Mean%3D%5Cdfrac%7B%5Ctext%7BSum%20of%20all%20obervation%7D%7D%7B%5Ctext%7BNumber%20of%20observation%7D%7D)
As it is given that Jack makes $12 on Monday, $14 on Tuesday, $18 on Wednesday, $16 on Thursday, $26 on Friday and $22 on Saturday. And we need to know how much he should earn on Sunday, so the average is $19. Therefore, we can write,
![\rm Mean=\dfrac{\text{Sum of all obervation}}{\text{Number of observation}}](https://tex.z-dn.net/?f=%5Crm%20Mean%3D%5Cdfrac%7B%5Ctext%7BSum%20of%20all%20obervation%7D%7D%7B%5Ctext%7BNumber%20of%20observation%7D%7D)
![19 = \dfrac{12+14+18+16+26+22+x}{7}\\\\133 = 108 + x\\\\133-108=x\\\\x = 25](https://tex.z-dn.net/?f=19%20%3D%20%5Cdfrac%7B12%2B14%2B18%2B16%2B26%2B22%2Bx%7D%7B7%7D%5C%5C%5C%5C133%20%3D%20108%20%2B%20x%5C%5C%5C%5C133-108%3Dx%5C%5C%5C%5Cx%20%3D%2025)
Hence, the amount that Jack has to earn in tips on Sunday if he wants to average $19 a day is $25.
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