Question

section 5: stem & leaf plot
the data below shows the number of times these 14 horses have raced in their careers:

horse name | number of times raced
mooney money | 5
smitty’s dream | 12
sir powell | 24
jumpin jacktee | 27
magic mete | 35
makybe musgrave | 31
princess degorski | 7

horse name | number of times raced
shanahan express | 45
pride of plumb | 20
slowpoke maclaren | 42
queen kesidis | 55
king christie | 25
galloping graham | 39
magilton the great | 22

a) use the data above to formulate an ordered stem and leaf plot (include a key).

stem | leaf
0 | 5,7
1 | 2
2 | 2,4,5,7 (handwritten with some unclear parts)
3 | 1,5,9 (handwritten)
4 | 2,5 (handwritten)
5 | 5 (handwritten)

b) use your table to identify the upper quartile, median, lower quartile and inter - quartile range.
(handwritten: median = 26, lq = 20, uq = 39, ir = 19 (with some crossed - out parts))
c) present this information in a box and whisker plot.

Explanation:

Step1: List all data values

5, 12, 24, 27, 35, 31, 7, 45, 20, 42, 55, 25, 39, 22

Step2: Sort data in order

5, 7, 12, 22, 24, 25, 27, 31, 35, 39, 42, 45, 55

Step3: Find median (n=14, average 7th & 8th)

Median = $\frac{27 + 31}{2} = 29$

Step4: Find lower quartile (Q1, median of first 7 values)

First 7: 5,7,12,22,24,25,27 → Q1=22

Step5: Find upper quartile (Q3, median of last 7 values)

Last 7: 31,35,39,42,45,55 → Q3=39

Step6: Calculate IQR (Q3-Q1)

IQR = 39 - 22 = 17

Answer:

Median = 29
Lower Quartile = 22
Upper Quartile = 39
Inter-Quartile Range = 17

(Note: For part c, a box and whisker plot would have: minimum=5, Q1=22, median=29, Q3=39, maximum=55. The box spans Q1 to Q3 with a line at the median; whiskers extend to min and max.)