What percentage of the general U.S. population are high-school dropouts? The Statistical Abstract of the United States, 120 th 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 95th percentile on the data. Locator \( = \) \( \square \) \[ 95 \mathrm{th} \text { percentile }=14 \] (c) Find the \( Q_{1} \) value on the data. \[ \text { Locator }=13 \] \[ Q_{1}=9 \] (d) Find the Q3 value on the data. \[ \text { Locator }=\square \] \[ Q_{3}=12 \] (e) Find the \( Q_{2} \) value on the data. \[ Q_{2}=10 \] (f) Find the \( I Q R \) of the data. \[ I Q R=3 \] (g) What are the Upper and Lower limits of the boxplot? \[ \text { Upper Limit }=16.5 \] Lower Limit \( =4.5 \) (h) With five-number-summary (in the order 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. o No outliers

To determine if there are any outliers in the dataset, we'll use the **Interquartile Range (IQR)** method. Here's a step-by-step breakdown: ### Given Five-Number Summary: - **Minimum (Min)**: 5 - **First Quartile (Q₁)**: 9 - **Median (Q₂)**: 10 - **Third Quartile (Q₃)**: 12 - **Maximum (Max)**: 15 ### Calculating the IQR: \[ \text{IQR} = Q₃ - Q₁ = 12 - 9 = 3 \] ### Determining the Upper and Lower Fences: - **Lower Fence**: \[ Q₁ - 1.5 \times \text{IQR} = 9 - (1.5 \times 3) = 9 - 4.5 = 4.5 \] - **Upper Fence**: \[ Q₃ + 1.5 \times \text{IQR} = 12 + (1.5 \times 3) = 12 + 4.5 = 16.5 \] ### Identifying Outliers: - **Lower Outliers**: Any data point below **4.5**. - **Upper Outliers**: Any data point above **16.5**. ### Applying to the Dataset: \[ \begin{array}{cccccccccccc} 5, & 6, & 7, & 7, & 7, & 7, & 8, & 8, & 8, & 8, & 8, & 9, \\ 9, & 9, & 9, & 9, & 9, & 9, & 10, & 10, & 10, & 10, & 10, & 10, \\ 10, & 10, & 11, & 11, & 11, & 11, & 11, & 11, & 11, & 12, & 12, & 12, \\ 12, & 13, & 13, & 13, & 13, & 13, & 13, & 14, & 14, & 14, & 14, & 14, \\ 15 \end{array} \] - **Minimum**: 5 (≥ 4.5) - **Maximum**: 15 (≤ 16.5) Since all data points fall within the range **4.5** to **16.5**, there are **no outliers** in this dataset. ### **Answer to Part (h):** **No outliers.**