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

To find the value of the additional data point, we calculate the sum of the existing data, use the new sample mean, and solve for the new data point. The calculation reveals that the additional data point is -239.329.

Step-by-step explanation:

To find the value of the additional data point, we need to use the given sample mean of the extended data set and the sum of the existing data points. First, let's calculate the sum of the given data points:

34 + 18 + 18 + 40 + 11 + 22 + 30 + 25 + 19 + 21 + 45 + 34 + 18 + 18 + 40 + 11 + 22 + 30 + 25 + 19 + 21 + 45 = 560

Let's denote the additional data point as 'x'. The new sample mean is 24.667, and there are now 12 + 1 = 13 data points with the new one included. The sum of the new data set will be 560 + x.

The mean of a data set is calculated by dividing the sum of all data values by the total number of data values. Thus, the equation for the new mean is:

(560 + x) / 13 = 24.667

Multiplying both sides by 13 gives us:

560 + x = 320.671

Now, subtract 560 from both sides to find the value of x:

x = 320.671 - 560

x = -239.329

Therefore, the value of the additional data point is -239.329.

Answer 2

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(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(487+x)/(21)\\\\x = 21(24.667)-487 = 31.007 \approx 31`

Thus, value of additional data point is 31