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Assume the sample below is a perfectly random sample of students at a school. How much greater is the mean of the reported heights at the school than the mean of the actual, measured heights at the school?

| Number | Reported Height | Measured Height | Difference |
|--------|------------------|-----------------|------------|
| 1 | 61 | 62 | -1 |
| 2 | 68 | 68 | 0 |
| 3 | 57.5 | 56.5 | 1 |
| 4 | 48.5 | 47 | 1.5 |
| 5 | 75 | 72 | 3 |
| 6 | 65 | 65 | 0 |
| 7 | 80 | 78 | 2 |
| 8 | 68 | 67 | 1 |
| 9 | 69 | 69.5 | -0.5 |
| 10 | 63 | 62.5 | 0.5 |

Calculate the mean difference.

Sagot :

GinnyAnswer
To find out how much greater the mean of the reported heights is compared to the mean of the actual, measured heights, we will go through the following steps:

1. Calculate the mean of the reported heights:

The reported heights are:
[tex]\[ 61, 68, 57.5, 48.5, 75, 65, 80, 68, 69, 63 \][/tex]

First, sum the reported heights:
[tex]\[ 61 + 68 + 57.5 + 48.5 + 75 + 65 + 80 + 68 + 69 + 63 = 655 \][/tex]

Next, count the number of reported heights, which is 10.

Now, calculate the mean:
[tex]\[ \text{Mean of reported heights} = \frac{655}{10} = 65.5 \][/tex]

2. Calculate the mean of the measured heights:

The measured heights are:
[tex]\[ 62, 68, 56.5, 47, 72, 65, 78, 67, 69.5, 62.5 \][/tex]

First, sum the measured heights:
[tex]\[ 62 + 68 + 56.5 + 47 + 72 + 65 + 78 + 67 + 69.5 + 62.5 = 647.5 \][/tex]

Next, count the number of measured heights, which is 10.

Now, calculate the mean:
[tex]\[ \text{Mean of measured heights} = \frac{647.5}{10} = 64.75 \][/tex]

3. Calculate the difference between the mean reported height and the mean measured height:

[tex]\[ \text{Mean difference} = 65.5 - 64.75 = 0.75 \][/tex]

Therefore, the mean of the reported heights is [tex]\(0.75\)[/tex] units greater than the mean of the measured heights.
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