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The waiting times, in minutes, for 16 patients at a dentist's surgery are recorded for a particular week (Week 1) on the following stem and leaf plot - Leaving Cert Mathematics - Question 5 - 2016
Question 5
The waiting times, in minutes, for 16 patients at a dentist's surgery are recorded for a particular week (Week 1) on the following stem and leaf plot. Key: 1 | 3 = ... show full transcript
Worked Solution & Example Answer:The waiting times, in minutes, for 16 patients at a dentist's surgery are recorded for a particular week (Week 1) on the following stem and leaf plot - Leaving Cert Mathematics - Question 5 - 2016
Step 1
Find the mode and the median of the data.
Answer
Mode Calculation
To find the mode, we identify which number appears most frequently in the data:
- From the stem-and-leaf plot for Week 1:
- 5 (1 time)
- 8 (2 times)
- 2 (3 times)
- 4 (3 times)
- 3 (2 times)
The number 2 and 4 both appear 3 times. Therefore, the mode is:
Mode = 12.
Median Calculation
To find the median, we list the waiting times in ascending order:
- 15, 18, 22, 22, 23, 23, 24, 24, 27, 32, 33, 38.
With 16 data points, the median will be the average of the 8th and 9th values:
Median = 24.
Step 2
Find the mean waiting time for Week 1, correct to 1 decimal place.
Answer
Mean Calculation
To calculate the mean waiting time for Week 1, we first sum all the waiting times provided in the stem-and-leaf plot:
-
Sum of waiting times = 5 + 8 + 22 + 22 + 23 + 24 + 27 + 32 + 33 + 40 + 44 + 44 = 363.
-
Since there are 16 patients, the mean is calculated as follows:
Rounding to 1 decimal place, we have:
Mean = 22.7.
Step 3
Show these results on the plot above (under Week 2), creating a back-to-back stem and leaf plot.
Answer
Values for Week 2
The results to display include:
- 27, 23, 6, 15, 18, 29, 16, 17, 15, 18, 40, 32, 16, 12, 28, 9.
Stem-and-Leaf Plot for Week 2
Week 2 data values will be ordered and displayed as follows:
Week 2 Week 1
0 | 6 8
1 | 2 5 5 7 8 8
2 | 3 3 4 4 4
3 | 0 2 8
4 | 0
9 |
Key: 1 | 3 = 13 minutes
This displays both weeks' data in relation to each other.