Life Expectancy Life expectancy for all the different countries in the world ranges from a low of only 52.2 years (in Sierra Leone) to a high of 84.7 yea (in Hong Kong). Life expectancies are clustered at the high end, with about half of all the countries having a life expectancy between about 74 and the maximum of 84.7 . A few countries, such as Sierra Leone, have a very low life expectancy. The full dataset is in AllCountries. Click here for the dataset associated with this question. (a) What is the shape of the distribution of life expectancies for all countries? Symmetric. Skewed to the right. Skewed to the left. None of these. eTextbook and Media (b) From the information given, estimate the median of the life expectancies. Round your answer to the nearest integer. Median = i eTextbook and Media (

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### (a) Shape of the Distribution

**Answer:** **Skewed to the left.**

**Explanation:**
- The distribution of life expectancies is **clustered at the high end** (around 74 to 84.7 years), with **a few countries having much lower life expectancies** (e.g., Sierra Leone at 52.2 years).
- **Skewness Direction:** 
  - **Skewed to the left** (negative skew) means the tail is on the lower end of the scale.
  - In this case, since most countries have higher life expectancies with a few lower outliers, the distribution has a tail extending to the left.

### (b) Estimating the Median

**Estimated Median:** **80 years**

**Explanation:**
- **Median Definition:** The median is the middle value that separates the higher half from the lower half of the data set.
- Given that **about half of all countries have a life expectancy between approximately 74 and 84.7 years**, the median would logically fall near the center of this range.
- **Calculation:** 
  - Average of 74 and 84.7: 
    $$
    \frac{74 + 84.7}{2} = 79.35 \approx 80 \text{ years (rounded to the nearest integer)}
    $$
- Therefore, the **median life expectancy is estimated to be around 80 years**.
### (a) Shape of the Distribution **Answer:** **Skewed to the left.** **Explanation:** - Most countries have higher life expectancies with a few having much lower ones, causing the distribution to have a tail on the lower end. ### (b) Estimating the Median **Estimated Median:** **80 years** **Explanation:** - The median life expectancy is approximately 80 years, based on the range of 74 to 84.7 years for half of the countries.

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