Ans: (a) Median $=57$, range $=52$, inter-quartile range $=22$ (b) (i) Yes (ii) Yes
- The median $=57$
The range $= 75 – 23 = 52$
The inter-quartile range $=65 – 43 = 22 $
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- Note that the range and the inter-quartile range of the distribution of scores in the second survey are $34$ and $17$ respectively, which is smaller than that of the first survey (i.e. $52$ and $22$ respectively). Therefore, the distribution of scores in the second survey is less dispersed than the first survey.
- Note that the lowest score in the second survey (i.e. $44$) is higher than the lower quartile of the first survey (i.e. $43$). Therefore, at least $25\%$ of these students have a greater extent of satisfaction shown in the second survey than the first survey. Hence, I agree.
