The next class is taking the SAT exam and their scores are listed below. What is the IQR, and Standard Deviation of this set of data?
Eleven students from another class (Group 2) in the same school took the SAT. Here are their scores. Calculate the mean, quartiles, interquartile range, standard deviation, the median, maximum and minimum scores. Use these values to make a boxplot.
| Minimum | |
| Quartile 1 | |
| Median | |
| Quartile 3 | |
| Maximum | |
| Mean | |
| Interquartile Range |
|
| Standard Deviation |
| Student SAT Scores |
\(\mathsf{x_i - \bar x }\) | \(\mathsf{(x_i - \bar x)^{2}}\) |
| 1400 | ||
| 1500 | ||
| 1600 | ||
| 1775 | ||
| 1795 | ||
| 1805 | ||
| 1930 | ||
| 1960 | ||
| 1960 | ||
| 1965 | ||
| 2055 |
1. List the minimum, quartile 1, median, quartile 3, and maximum in the table.
2. Use these values to make the box plot.
3. Calculate the interquartile range. Q3 – Q1.
4. Calculate the mean and subtract it from each value. \(\mathsf{x_i - \bar x }\)
5. Square the values in column 2. \(\mathsf{(x_i - \bar x)^{2}}\)
6. Find the sum of the squares
7. Find the average of the sum of squares.
8. Calculate the standard deviation.
| Minimum | 1400 |
| Quartile 1 | 1600 |
| Median | 1805 |
| Quartile 3 | 1960 |
| Maximum | 2055 |
| Mean | 1795 |
| Interquartile Range |
360 |
| Standard Deviation |
202.4 |
| Student SAT Scores | \(\mathsf{x_i - \bar x }\) | \(\mathsf{(x_i - \bar x)^{2}}\) |
| 1400 | -395 | 156025 |
| 1500 | -295 | 87025 |
| 1600 | -195 | 38025 |
| 1775 | -20 | 400 |
| 1795 | 0 | 0 |
| 1805 | 10 | 100 |
| 1930 | 135 | 18225 |
| 1960 | 165 | 27225 |
| 1960 | 165 | 27225 |
| 1965 | 170 | 28900 |
| 2055 | 260 | 67600 |
| 450750 | ||
| 40977.27 | ||
| 202.4 |
