Unit 4 sec 4.4 Investigating spread

Unit 4 sec 4.4 Investigating spread

13 January 2016

22:52

Just as dataplotter provided instant summary measures of location (the mean and the median), it also provided the 3 summaries of spread introduced in this section: range, interquartile range and standard deviation.

So, taking the mean and median together with the range, interquartile range and standard deviation, conclusions can be drawn. There is evidence that:

v people tend to think that the word probable indicates, the higher degree of likelihood than the words possible. (A conclusion based on comparing locations).

v There is a greater degree of agreement on the meaning of the word probable than the meaning of the word possible. (A conclusion based on comparing spreads).

As a footnote to this investigation, one of the students who carried out the study, commented on the meaning of the word possible rather depends on the tone of the boys used when saying get and also on the context. Another said that there was so much variation in its interpretation that possible really seen to be a useless word for conveying meaning and should be dropped from the vocabulary.

 Following on from section 3, where you looked at

summarising a dataset by measuring its location, this section worked at measures of spread. Three particular measures of spread were looked at in detail.

Ø The range of a set of numbers is found by calculating max -min.

Ø The interquartile range (IQR) is the range of the middle half of the data and is calculated as Q3 -Q1 (where Q3 is the upper quartile and Q1 is the lower quartile).

Ø The standard deviation (SD) is the square root of the mean of the square is of the deviations of each data value from the mean. (You were also briefly introduced to a 4^th measure of spread, the variance, which is the square of the standard deviation.)

These 3 main measures of spread (range, interquartile range and standard deviation) were used as part of the investigation of the possible, and probably datasets to demonstrate that there seemed to be a greater measure of agreement on the meaning of the word probably than on the meaning of the word possible.