Q 17. - The Practice of Statistics for AP

Question

Going to school Students in a high school statistics class were given data about the primary method of transportation to school for a group of $30$ students. They produced the pictograph shown.

(a) How is this graph misleading?

(b) Make a new graph that isn’t misleading.

Step-by-Step Solution

Answer

Part (a) The graph violates the area principle through the bus and car ratio.

Part (b) Here, is the graph that isn’t misleading. 

Part (a) Step 1: Given Information

Each group contains $30$ students overall. The pictograph is in below,produced by them is:

Part (a) Step 2: Concept

The distribution of a category variable is displayed using pie charts and bar graphs. Any set of quantities measured in the same units can be compared using bar graphs. It's a good idea to ask yourself, "What do I see?" when looking at any graph. 

Part (a) Step 3: Explanation

The diagrammatical depiction of one car represents two cars, one bus indicates seven bus riders, and one walker indicates two walkers in the following pictogram representation. Because each variable's percentage varies, it's difficult to gather and shape data. However, when analysing data using a bar graph, the eyes react to the area of the bars as well as their height, giving the correct impression. As a result of the bus and automobile ratio, the graph violates the area principle.

Part (b) Step 1: Explanation

The bar graph would be able to depict the genuine distribution of data on the principal mode of school transportation. Below is a bar graph for the given data.

Hence, the above graph isn't misleading.