What percentage of the general U.S. population are high-school dropouts? The Statistical Abstract of the United States, 120th Edition, gives the percentage of high-school dropouts by state. For convenience, the data are sorted in increasing order. \[ \begin{array}{c} 5,6,7,7,7,7,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,11,11,11,11,11 \\ 11,11,12,12,12,12,13,13,13,13,13,13,14,14,14,14,14,15 \end{array} \] (a) Which percentile is the value 10 ? (Round to the nearest whole value above-) 10 is the \( \square \) th percentile. (b) Find the 95 th percentile on the data. Locator \( = \) \( \square \) 95th percentile \( = \) \( \square \) (c) Find the Q1 value on the data. Locator \( = \) \( \square \) \( Q_{1}= \) \( \square \) (d) Find the Q3 value on the data. Locator \( = \) \( \square \) \( Q_{3}= \) \( \square \) (e) Find the \( Q_{2} \) value on the data. \( Q_{2}= \) \( \square \) (f) Find the \( I Q R \) of the data. \( I Q R= \) \( \square \) (g) What are the Upper and Lower limits of the boxplot? Upper Limit \( = \) \( \square \) Lower Limit \( = \) \( \square \) (h) With five-number-summary (in the order \( \operatorname{Min}=Q_{1}=Q_{2}=Q_{3}-\operatorname{Max} \) ) being 5-9-10=12= 15 , are there any outliers? The only outlier is 5 The only outlier is 15 Outliers are 15 , and 14 Outliers are 5, and 15. No outliers

To determine the percentiles from your data, we first note that there are 50 values in the dataset. When looking for the position of the 10th value, we can use the formula: \[ P = \frac{n}{100} \times k + 1 \] where \( n \) is the number of observations and \( k \) is the percentile. For 10, the position is \( P = \frac{50}{100} \times 10 + 1 = 6 \). The 6th value from the sorted data is 8, which appears multiple times. Thus, 10 falls in the range that includes the 11th value, making it the 60th percentile. For the 95th percentile, we calculate the position as follows: \[ P = \frac{50}{100} \times 95 + 1 = 48.5 \] This means we average the 48th and 49th values in sorted order to get \( 14 \) (both share the same value). For the interquartile range (IQR), we find \( Q_1 \) and \( Q_3 \). The \( Q_1 \) position is calculated by \( P = \frac{50}{100} \times 25 + 1 = 13 \) (which gives 9), while \( Q_3 \) is \( P = \frac{50}{100} \times 75 + 1 = 39 \) (gives 14). Hence, IQR is \( 14 - 9 = 5 \). The upper limit for potential outliers can be determined as \( Q_3 + 1.5 \times IQR = 14 + 7.5 = 21.5 \) and the lower limit as \( Q_1 - 1.5 \times IQR = 9 - 7.5 = 1.5 \). Since both 5 and 15 fall outside of these limits, they are outliers. So the calculations lead to: 10 is the **60th percentile**. 95th percentile is located at position **49**, value **14**. The first quartile \( Q_1 = 9 \). The third quartile \( Q_3 = 14 \). \( Q_2 = 10 \). The IQR is **5**. Upper limit **21.5**, Lower limit **1.5**. Outliers identified are **5** and **15**. Fun fact: Education shapes futures! Countries that invest in education often see better economic outcomes, making high-school completion a vital step towards prosperity. In practical scenarios, understanding these statistics helps in creating targeted interventions, such as mentorship programs to reduce dropout rates, ensuring each student has the support they need to succeed!