Question

The number of defects in the first five cars to come through a new production line are 9, 7, 10, 4, and 6, respectively. If the sixth car through the production line has either 3, 7, or 12 defects, for which of these values does the mean number of defects per car for the first six cars equal the median?

Answer 1

the number of defect in the sixth car is 3

Explanation:

Data provided in the question:

The number of defects in the first five cars

9

7

10

4

6

Now out of the given choices for defect in sixth car i.e 3, 7, 12

considering the first choice 3

thus, mean =
`\frac{\textup{Sum of all the observations}}{\textup{Total number of observations}}`

=
`\frac{\textup{3+9+7+10+4+6}}{\textup{6}}`

=
`\frac{\textup{39}}{\textup{6}}`

= 6.5

now for the median arranging the data in ascending order

3, 4, 6, 7, 9, 10

since, the number of observations are even,

the median will be

=
`\frac{\textup{6 + 7}}{\textup{2}}`

=
`\frac{\textup{13}}{\textup{2}}`

= 6.5

According to the condition given in the question, the mean and the median are equal,

therefore,

the number of defect in the sixth car is 3