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

Question

UpStudy AI · Accepted Answer

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.**
There are no outliers in the dataset.

Real Tutor Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Statistics Questions