Question

interpreting dot plots sheet 2

1. this dot plot shows the number of minutes it takes captain to cycle to work each day.

for each of the following statements state whether they are true, false or unknown.
a) the longest it took him to get to work was 28 minutes.
b) most of the time it took him at least 20 minutes to get to work.
c) his median journey time was 19 minutes.
d) his journey was quicker when there was less traffic on the roads.
e) his mean journey was 19 minutes.
f) the range of his journey times was 12 minutes.

Explanation:

Step1: Analyze statement a

Count the number of dots at each value. There is a dot at 28. So the longest time is 28 minutes.

Step2: Analyze statement b

Count the number of dots for values ≥ 20. There are 1 + 1+ 2+ 1+ 1+ 1 = 7 dots for ≥ 20. Total dots: 1+1 + 2+1+3+1+1+2+1+1+1 = 16. 7 < 8 (half of 16). So it's false.

Step3: Analyze statement c

Arrange the data in order (15,16,17,17,18,19,19,19,20,21,22,22,23,25,27,28). There are 16 data points. The median is the average of 8th and 9th values. 8th value is 19, 9th value is 20. Median = (19 + 20)/2=19.5 ≠ 19. False.

Step4: Analyze statement d

The dot - plot only shows journey times, no information about traffic. Unknown.

Step5: Analyze statement e

Calculate the mean: \((15\times1 + 16\times1+17\times2 + 18\times1+19\times3+20\times1+21\times1+22\times2+23\times1+25\times1+27\times1+28\times1)\div16=(15 + 16+34 + 18+57+20+21+44+23+25+27+28)\div16=(15+16+34+18+57+20+21+44+23+25+27+28)=328\). Mean \(=\frac{328}{16}=20.5
eq19\). False.

Step6: Analyze statement f

Range = Max - Min. Max = 28, Min = 15. Range = 28 - 15=13≠12. False.

Answer:

a. True
b. False
c. False
d. Unknown
e. False
f. False