Chapter 1.3, Problem 112E

To determine

To describe: the shape, center and spread of the distribution of the graph.

Answer to Problem 112E

Shape: symmetric and is not skewed.

Centre: $170\text{cm}$

Spread: from 145.5 that is the smallest value to 191 which is the highest value.

Outliers: There are no outliers in the data

Explanation of Solution

Given:

Heights of 50 randomly selected Canadian students.

Calculation:

Shape: the peak of the dot-plot is at 170 . It indicates that the 4 students have 170 cm height. Thus $170\text{cm}$ is the Mode. Most of the students have height between $160\text{cm}$ to $180\text{cm}$ . The distribution is almost symmetric and is not skewed.

Centre: The centre that divides the observations into two equal parts i.e. median, so that about half take larger values and about half take the smaller values. In this data, the median is about$170\text{cm}(169.88\text{cm})$

Spread: The spread of the distribution tells us the variability that is there in the data. One way of describing the spread is to give largest and smallest value. The spread of the given data is from 145.5 that is the smallest value to 191 which is the highest value. Instead, we can find out range by subtracting smallest value from the largest value. Here the range would be $191-145.5=45.5\text{cm}$

Outliers: There are no outliers in the data, though there are values i.e. 143 and 150 which are somewhat different from the overall pattern. However, they do not clearly stand apart from the rest of the distribution.

Conclusion:

Shape: symmetric and is not skewed.

Centre: $170\text{cm}$

Spread: from 145.5 that is the smallest value to 191 which is the highest value.

Outliers: There are no outliers in the data