What is the mean of the reported heights listed in the table below?

| Number | Reported Height |
|--------|------------------|
| 1 | 61 |
| 2 | 68 |
| 3 | 57.5 |
| 4 | 48.5 |
| 5 | 65 |
| 6 | 80 |
| 7 | 68 |
| 8 | 69 |
| 9 | 63 |
| 10 | |



Answer :

To calculate the mean of the reported heights, follow these steps:

1. Identify the reported heights: Extract the reported heights from the table:
- [tex]\(61\)[/tex]
- [tex]\(68\)[/tex]
- [tex]\(57.5\)[/tex]
- [tex]\(48.5\)[/tex]
- [tex]\(65\)[/tex]
- [tex]\(80\)[/tex]
- [tex]\(68\)[/tex]
- [tex]\(69\)[/tex]
- [tex]\(63\)[/tex]

2. Remove any missing entries: Ensure that only valid numeric entries are included. Here, the 10th row is empty and should be excluded.

3. Sum the valid reported heights:
[tex]\[ 61 + 68 + 57.5 + 48.5 + 65 + 80 + 68 + 69 + 63 \][/tex]

4. Count the number of valid reported heights: In this case, there are 9 valid entries.

5. Calculate the mean: Divide the sum of the valid reported heights by the number of entries.

6. The sum of the reported heights [tex]\(S\)[/tex]:
[tex]\[ S = 61 + 68 + 57.5 + 48.5 + 65 + 80 + 68 + 69 + 63 = 580 \][/tex]

7. Number of entries [tex]\(N\)[/tex]:
[tex]\[ N = 9 \][/tex]

8. Mean of the reported heights [tex]\(\mu\)[/tex]:
[tex]\[ \mu = \frac{S}{N} = \frac{580}{9} \approx 64.44444444444444 \][/tex]

Therefore, the mean of the reported heights is approximately [tex]\(64.44444444444444\)[/tex].