Question

A data set consists of the data given below plus one more data point. When the additional point is included in the data set the sample mean of the resulting data set is 24.667. What is the value of the additional data point?

34, 18, 18, 40, 11, 22, 30, 25, 19, 21, 45 34, 18, 18, 40, 11, 22, 30, 25, 19, 21, 45

Value of additional data point: ________

Answer 1

Answer:

Value of additional data point is 31.

Step-by-step explanation:

We are given the following data set:

34, 18, 18, 40, 11, 22, 30, 25, 19, 21, 45 34, 18, 18, 40, 11, 22, 30, 25, 19, 21, 45

Formula:

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{487}{20} = 24.35$

The old mean is 24.35

A new data was added in the data. The new mean is 24.667

We have to find the value of additional point.

Let x be the added point in the data set.

Thus, we can write:

$24.667 = \displaystyle\frac{487+x}{21}\\\\x = 21(24.667)-487 = 31.007 \approx 31$

Thus, value of additional data point is 31