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].
