## Stem and Leaf Graphs Answers

1.a.

b. Median = 2695 m
Upper quartile = 3195 m
Lower quartile = 2040 m

c. Interquartile range = 1155 m

2. a.

 Depths of New Zealand Caves (m) 8 89 7 13 21 49 75 6 5 40 4 00 15 3 07 15 15 46 57 62 94 Note       ]5[ 40 means 540 m

b. There are 15 depths so the median is the 8th depth. This is 400

The quartile is the 4th depth (from top and bottom). The upper quartile is 721. The lower quartile is 346

The interquertile range = upper quartile − lower quartile= 721 − 346 = 375

3. a.

 Lengths of Metro systems (km) 4 30 92 3 32 44 2 44 78  73  44  32  27  15 1 10    21    41    70 65   64   61 0 72    72    92   98 N. and S. America and Asia Note       ]3[ 78 means 378 m Europe

b. There are 11 lengths so the median is the 6th depth. This gives 132 and 121 respectively.

The quartile is the 3rd length (from top and bottom) The upper quartiles are 178and 244. The lower quartiles are 65 and 92

4.

The median for the 17 lengths is the 9th length. This is 177 km. The lower quartile is halfway between the 4th and 5th length which is 159.5 km. The upper quartile is halfway between the 13th and 14th length which is 198 km

5.a.

b. The median for the 19 results is the 10th result. This is 56 and 55. The lower quartile is the 5th result which is 43 and 42. The upper quartile is the 15th result which is 73 and 66.

c. The distributions of the results are similar with the medians and lower quartiles being almost the same. However the First class would appear to have done better at the higher end with a higher upper quartile and 6 results above 70 as opposed to only 3 above 70 in the Second class.