Question

a grocer thought her eggs needed safer packaging. she counted the number of intact eggs in 24 cartons from the cooler. the dot plot below shows her results: dot - plot image not included in ocr. describe the distribution of intact eggs. shape: the distribution of intact eggs is skewed to the left. center: the median of the intact eggs is 11.5 eggs. spread: the range of the intact eggs is 6 eggs. outliers: there are 0 potential outliers.

Explanation:

Step1: Determine shape

The tail of the dot - plot extends to the left, so it is skewed to the left.

Step2: Calculate median

There are $n = 24$ data points. The median is the average of the 12th and 13th ordered data points. Counting the dots: 1 dot at 6, 0 dots at 7, 0 dots at 8, 1 dot at 9, and then starting from 12, we count. The 12th and 13th values are both 12, so the median is $\frac{12 + 11}{2}=11.5$ (assuming we order the data and consider the cumulative count).

Step3: Find range

The maximum value is 12 and the minimum value is 6. Range=Maximum - Minimum. So range = $12-6 = 6$.

Step4: Check for outliers

Using the 1.5×IQR (Inter - Quartile Range) rule, first find Q1 and Q3. Since $n = 24$, the lower half of the data (first 12 values) has a median (Q1) and the upper half (last 12 values) has a median (Q3). After analyzing the distribution, we find no values that are far enough from the quartiles to be considered outliers. So there are 0 outliers.

Answer:

Shape: skewed to the left
Center: 11.5
Spread: 6
Outliers: 0