# Using Statistics to Interpret Categorical and Quantitative Data

By Tara Mason on Apr 25, 2017

Student will increase understanding of how we use statistics to interpret numerical data (quantitative) by using a real world example and tactual media.

## Procedure

For this lesson, using a real world topic to intrepret data on a simple tactile graph will help reinforce these skills in a student's math class. An example is presented below that could be used to illustrate how to compare two frequency distributions.

1. Twenty-one heavy smokers compared to twenty-one non-smokers. The two groups were put on a treadmill at the fastest setting and the time in seconds was measured until they fell off from exhaustion.

• Group A (Smokers): 18,16,18,24,23,22,22,23,26,29,32,34,34,36,36,43,42,49,46,46,57
• Group B (Non-smokers): 120, 95, 95, 95, 160, 160, 200, 250, 100, 100, 200, 220, 250, 250, 95, 100, 200, 250,300, 200, 250

2. Using Talking graphing calculator compute the mode, median, mean

3. Using braille graph paper, layout the numbers in order to figure out the upper and lower quartiles, range and interquartile range

4. Create two simple tacile graphs using braille graph paper to compare the interquartile range of Group A and Group B

5. Discuss the various strategies used to compare these two groups.

For example, when we use mean how is it effected by extreme numbers on the top or the bottom of the set? Or, Does the median give us an accurate estimate of how well Group A performed or Group B performed? How can a tactile graph of each average finding give us information to use when comparing these two groups?

*Problem set modified from Andy Fields, Discovering Statistics Using SPSS (2009).

The tactile bar graph is used with the permission of Gwyn McCormack and Positive Eye.  Visit: http://www.positiveeye.co.uk/