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# 4, 13, 5, 8, R, 5, 11

In the data set shown, R is an integer. If the median of the data set is 8 and R < 11, what is a possible value of R?

## The correct answer is: 8, 9, &10

### Median (for odd number of observations) = Value of the Observation

Step-by-step solution:-

Median (for odd number of observations) = Value of the Observation

In the given data set, no. of observations = n = 7

∴ Median = value of observation

∴ Median = value of 4^{th} observation

Median = 8 .______________ (Given)

∴ Value of 4th observation = 8

We are given that R < 11 but Median is the 4th digit which is 8 so R cannot be less than 8

Therefore, the possible values of R are - 8, 9 & 10

Final Answer:-

∴ The possible values of R are 8, 9 & 10

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