Question

Show that the mean and median of (√ 3, √ 12, √ 48), and (√ 75) are equal.

a) True
b) False

Answer 1

After calculating, both the mean and median of the set (√3, √12, √48, √75) approximate to 5.196, hence the statement that the mean and median are equal is true.

Step-by-step explanation:

Let's calculate the mean and median of the given numbers: √3, √12, √48, and √75.

• First, find the mean by adding all numbers and dividing by the total count:
  Mean = (√3 + √12 + √48 + √75) / 4
• Next, calculate the median, which is the middle number when they are listed in order. Since there are an even number of terms, the median is the average of the two middle numbers:
  Median = (√12 + √48) / 2

We need to simplify and compare these values to confirm if they are indeed equal.

Step-by-step simplification:

1. √3 = 1.732...
2. √12 = 2 √3 = 3.464...
3. √48 = 4 √3 = 6.928...
4. √75 = 5√3 = 8.660...
5. Calculate the mean:
   Mean = (1.732 + 3.464 + 6.928 + 8.660) / 4 = 20.784 / 4 = 5.196 (approx)
6. Calculate the median:
   Median = (3.464 + 6.928) / 2 = 10.392 / 2 = 5.196 (approx)

The calculated mean and median are approximately equal, which means the statement is true.