Question

Travis is testing how far he can throw a baseball to prepare himself for the season. He makes 16
throws and records the length of each throw in feet. The results are provided in the accompanying table.

236
240
232
242
238
235
228
245

247
239
234
238
241
227
243
238

Travis says that the histogram provided below could be used to represent the data.

A histogram has a horizontal axis labeled Distance in feet that goes from 220 to 260 in increments of 5 and a vertical axis labeled Frequency that goes from 0 to 8 in increments of 1. Five bars of width 5 extend from the horizontal axis, starting at horizontal axis value 230. The heights of the bars are as follows, where the left horizontal axis value is listed first and the height is listed second: 230, 2; 235, 2; 240, 6; 245, 4; 250, 2.

Show whether the histogram Travis created is correct and, if not, explain how the histogram could be corrected.

Answer 1

The histogram Travis created is not correct. The histogram should have bars representing the frequency of each distance range.

To correct the histogram, we should first identify the frequency of each distance range. Counting the number of throws falling into each range, we get:

- 230-234: 4 throws
- 235-239: 7 throws
- 240-244: 3 throws
- 245-249: 2 throws

Based on these frequencies, the correct histogram should have bars representing these ranges with the corresponding heights. The corrected histogram should have bars at 230, 235, 240, and 245, with heights of 4, 7, 3, and 2 respectively. The bars should start at the horizontal axis value and extend upwards based on the frequency. The histogram should accurately represent the distribution of the data.