A dataset has 1000 records and 50 variables with 5% of the values missing, spread randomly throughout the records and variables.

Response:

Average = 2000

Step-by-step breakdown:

The numbers provided are:

1,000 2,300 2,600

To calculate the average:

Initially, round each number to the nearest 1000, then determine the average.

Solution:

1000 is already rounded, so it stays the same.

To round to the nearest thousand, check the hundred's digit.

• If the hundred’s digit exceeds 5, the thousand’s digit increases by 1, and the hundred’s digit is set to 0.

• If it’s less than 5, the thousand’s digit remains the same, changing the hundred’s digit to 0.

Thus, 2300 rounds to 2000.

and 2600 rounds to 3000.

Consequently, the numbers for averaging are 1000, 2000, 3000.

The formula for average is as follows:

upon applying the formula:

So, the average after rounding to the nearest 1000 is 2000.

Answer:

Let the train's speed be denoted as x km/h.

Scenario 1:

Distance = 288 km

Speed = x km/h

Time = Distance divided by Speed

= 288/x hours

Scenario 2:

Distance = 288 km

Speed = (x + 4) km/h

Time = 288/(x + 4) hours

As 288/x is greater than 288/(x + 4)

288/x - 288/(x + 4) = 1

288[1/x - 1/(x + 4)] = 1

[x + 4 - x] / [x(x + 4)] = 1/288

[4 / (x^2 + 4x)] = 1/288

x² + 4x = 1152

x² + 4x - 1152 = 0

x² + 36x - 32x - 1152 = 0

x(x + 36) - 32(x + 36) = 0

(x + 36)(x - 32) = 0

x + 36 = 0, x - 32 = 0

x = -36, x = 32

x = -36 is not valid as speed cannot be negative.

Conclusively, the train's speed = 32 km/h

The graph indicates that x never goes below 0. This means the point (-1,0) is not included in the graph. Therefore, D is the only valid option.