Line 3,731: |
Line 3,731: |
| spread. So we calculate range as: | | spread. So we calculate range as: |
| | | |
− |
| |
− |
| |
− |
| |
− |
| |
− |
| |
| Range = maximum value - minimum value | | Range = maximum value - minimum value |
− |
| |
− |
| |
− |
| |
− |
| |
− |
| |
| | | |
| For example, let us consider the following data | | For example, let us consider the following data |
Line 3,749: |
Line 3,739: |
| 23 56 45 65 59 55 62 54 85 25 | | 23 56 45 65 59 55 62 54 85 25 |
| | | |
− |
| |
− |
| |
− |
| |
− |
| |
− |
| |
| The maximum value is 85 and the minimum value is | | The maximum value is 85 and the minimum value is |
| 23. This results in a range of 62, which is 85 minus 23. Whilst using | | 23. This results in a range of 62, which is 85 minus 23. Whilst using |
Line 3,765: |
Line 3,750: |
| your study and your range is 7 to 123 years old you know you have | | your study and your range is 7 to 123 years old you know you have |
| made a mistake! | | made a mistake! |
− |
| |
− |
| |
| | | |
| | | |
Line 3,772: |
Line 3,755: |
| | | |
| | | |
− |
| |
− |
| |
− |
| |
| Quartiles tell us about the spread of a data set | | Quartiles tell us about the spread of a data set |
| by breaking the data set into quarters, just like the median breaks | | by breaking the data set into quarters, just like the median breaks |
Line 3,780: |
Line 3,760: |
| below, which have been ordered from the lowest to the highest scores, | | below, which have been ordered from the lowest to the highest scores, |
| and the quartiles highlighted in red. | | and the quartiles highlighted in red. |
− |
| |
− |
| |
− |
| |
− |
| |
| | | |
| | | |
Line 3,848: |
Line 3,824: |
| | | |
| 20th 42 40th 52 60th 64 80th 74 100th 85 | | 20th 42 40th 52 60th 64 80th 74 100th 85 |
− |
| |
− |
| |
− |
| |
− |
| |
− |
| |
− |
| |
− |
| |
− |
| |
| | | |
| | | |
Line 3,863: |
Line 3,831: |
| and 76th student's marks. Hence: | | and 76th student's marks. Hence: |
| | | |
− |
| |
− |
| |
− |
| |
− |
| |
− |
| |
| First quartile (Q1) = 45 + 45 ÷ 2 = 45 | | First quartile (Q1) = 45 + 45 ÷ 2 = 45 |
| | | |
Line 3,876: |
Line 3,839: |
| Third quartile (Q3) = 71 + 71 ÷ 2 = 71 | | Third quartile (Q3) = 71 + 71 ÷ 2 = 71 |
| | | |
− |
| |
− |
| |
− |
| |
− |
| |
− |
| |
| In the above example, we have an even number of | | In the above example, we have an even number of |
| scores (100 students rather than an odd number such as 99 students). | | scores (100 students rather than an odd number such as 99 students). |
Line 3,890: |
Line 3,848: |
| recognize that the second quartile is also the median. | | recognize that the second quartile is also the median. |
| | | |
− |
| |
− |
| |
− |
| |
− |
| |
− |
| |
| Quartiles are a useful measure of spread because | | Quartiles are a useful measure of spread because |
| they are much less affected by outliers or a skewed data set than the | | they are much less affected by outliers or a skewed data set than the |
Line 3,906: |
Line 3,859: |
| the scores in the distribution. Hence, for our 100 students: | | the scores in the distribution. Hence, for our 100 students: |
| | | |
− |
| |
− |
| |
− |
| |
− |
| |
− |
| |
| Interquartile range = Q3 - Q1 | | Interquartile range = Q3 - Q1 |
| | | |
Line 3,919: |
Line 3,867: |
| = 26 | | = 26 |
| | | |
− |
| |
− |
| |
− |
| |
− |
| |
− |
| |
| However, it should be noted that in journals and | | However, it should be noted that in journals and |
| other publications you will usually see the interquartile range | | other publications you will usually see the interquartile range |
| reported as 45 to 71, rather than the calculated range. | | reported as 45 to 71, rather than the calculated range. |
| | | |
− |
| |
− |
| |
− |
| |
− |
| |
− |
| |
| A slight variation on this is the | | A slight variation on this is the |
| semi-interquartile range, which is half the interquartile range = ½ | | semi-interquartile range, which is half the interquartile range = ½ |
| (Q3 - Q1). Hence, for our 100 students, this would be 26 ÷ 2 = 13. | | (Q3 - Q1). Hence, for our 100 students, this would be 26 ÷ 2 = 13. |
| | | |
− |
| |
| == Standard Deviation == | | == Standard Deviation == |
| | | |