Q. 2.165 - Elementary Statistics

Question

Each year the director of the reading program in a school district administers a standard test of reading skills. Then the director compares the average score for his district with the national average. The figure presented to the school board in the year 2013.

a. Obtain a truncated version of Fig. by sliding a piece of paper over the bottom of the graph so that the bars start at $16$ .

b. Repeat part (a), but have the bars start at $18$.

c. What misleading impression about the year 2013 scores is given by the truncated graphs obtained in parts (a) and (b)?

Step-by-Step Solution

Answer

(a) Adjust the graph's horizontal axis so that the bar begins at 16.

(b) Adjust the graph's horizontal axis so that the bar begins at 18.

(c) It appears that the district average is significantly greater than the national average, but this is not the case.

Part (a) Step 1: Given information

The given data is

Part (a) Step 2: Explanation

The $y$ axis of a truncated graph does not begin at $0$. These graphs might provide the impression of significant change when there is actually very little. While truncated graphs can be useful for overdrawing differences or saving space, they are frequently avoided.

Move the horizontal axis of the graph such that the bar starts at $16$,

Part (b) Step 1: Given information

The given data is

Part (b) Step 2: Explanation

Move the horizontal axis of the graph such that bar starts at $18$,

Part (c) Step 1: Given information

The given data is

Part(c) Step 2: Explanation

It appears that the district average is significantly greater than the national average, but this is not the case. The graph in part (a) implies that the district mean is roughly double the 2013 average wage, which is not the case.

Part (b) of the graph assumes that the average district normal in 2013 is nearly $5\%$, which is not the case.