Question

1. the following is based on a study used to find the amount of hate crimes in the most populated cities in a certain state. dotplot a. what does the dot at 2 represent? outlier b. what proportion of cities have a crime rate below 100,000. majority 95% c. describe the distribution (include shape, center, spread, and outliers). right skewed, center (-0.6, -0.7) spread (1), outlier(2)

Explanation:

Step1: Interpret dot - plot value

In a dot - plot, each dot represents a data point. The dot at 2 is far from the majority of the data points, so it represents an outlier.

Step2: Analyze crime rate proportion

The question seems to have a mis - statement. The x - axis is labeled "Crimes (per 100,000)", so we assume the question means proportion of cities with crime rate less than some non - zero value. However, if we assume the question is about proportion of cities with crime rate less than 1 (per 100,000), we need to count the dots. But since no data on total number of dots is given precisely, we can't calculate a numerical proportion. If we assume the answer is based on visual inspection, we can't be sure it's 95%. A proper way would be to count all dots (total number of cities, say $n$) and dots with value less than 1 (say $m$) and calculate $\frac{m}{n}$.

Step3: Describe distribution

The distribution is right - skewed as the tail of the data extends to the right (towards higher values). To estimate the center, we can think of the median or mean. Without exact data values, we can say it's in the range where most of the data is concentrated, say around 0.6 - 0.7 (per 100,000). The spread can be estimated by looking at the range of non - outlier data, which seems to be around 1 (from near 0 to near 1 per 100,000). The outlier is the value at 2 (per 100,000).

Answer:

a. An outlier in the data set of hate - crime rates (per 100,000) for the cities.
b. Cannot be accurately determined without counting all dots in the dot - plot.
c. Right - skewed distribution. Center is approximately in the range 0.6 - 0.7 (per 100,000). Spread is approximately 1 (per 100,000). Outlier is at 2 (per 100,000).