Mcdonald Ayala
07/06/2023 · Senior High School
We measured the flat area of 30 apartments and we have measured the following values in \( \mathrm{m}^{2} \) : \( 82.6,57.3,70.4,65,48.4,103.8,73.6,43.5,66.1,93,52.6,70,84.2,55,81.3,61.5,75.1,34.8 \), \( 62.4,116,70.1,63.6,93,59.2,65.9,77.2,52.8,68.7,79.2,87.4 \). a) Create a table of grouped frequency distribution for the number of classes \( k=9 \). b) Construct a histogram of relative frequencies of the flat areas. c) From the specified values estimate the sample mean and the variance. d) From the middle values of the intervals and from their frequencies estimate the sample mean and the variance.
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a) The grouped frequency distribution table with 9 classes is as follows:
| Interval | Lower Limit | Upper Limit | Frequency |
|----------|-------------|-------------|-----------|
| 1 | 34.8 | 44.8 | 2 |
| 2 | 44.8 | 54.8 | 3 |
| 3 | 54.8 | 64.8 | 4 |
| 4 | 64.8 | 74.8 | 5 |
| 5 | 74.8 | 84.8 | 4 |
| 6 | 84.8 | 94.8 | 3 |
| 7 | 94.8 | 104.8 | 2 |
| 8 | 104.8 | 114.8 | 1 |
| 9 | 114.8 | 124.8 | 0 |
b) The histogram of relative frequencies would show intervals on the x-axis and relative frequencies on the y-axis, with asterisks representing the relative frequencies.
c) The sample mean is approximately 77.75, and the sample variance is approximately calculated as described.
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