6 Last year Eleanor played 11 rounds of golf. Her scores were as follows:
\(79 , \quad 71 , \quad 80 , \quad 67 , \quad 67 , \quad 74 , \quad 66 , \quad 65 , \quad 71 , \quad 66 , \quad 64\).
- Calculate the mean of these scores and show that the standard deviation is 5.31 , correct to 3 significant figures.
- Find the median and interquartile range of the scores.
This year, Eleanor also played 11 rounds of golf. The standard deviation of her scores was 4.23, correct to 3 significant figures, and the interquartile range was the same as last year.
- Give a possible reason why the standard deviation of her scores was lower than last year although her interquartile range was unchanged.
In golf, smaller scores mean a better standard of play than larger scores. Ken suggests that since the standard deviation was smaller this year, Eleanor's overall standard has improved.
- Explain why Ken is wrong.
- State what the smaller standard deviation does show about Eleanor's play.