Certainly! Let's go through the calculations for both data sets.
### Data (a):
The data is presented in a stem-and-leaf plot format. First, we need to list out the data points:
- Stem 2: Leaves 6, 8 → Data points: 26, 28
- Stem 3: Leaves 1, 2, 3, 7 → Data points: 31, 32, 33, 37
- Stem 4: Leaves 5, 6 → Data points: 45, 46
- Stem 5: Leaves 1, 4, 8 → Data points: 51, 54, 58
So, the complete data set for (a) is: 26, 28, 31, 32, 33, 37, 45, 46, 51, 54, 58
#### i) Mode of data (a):
The mode is the value that appears most frequently in a data set.
- Checking the data set: 26, 28, 31, 32, 33, 37, 45, 46, 51, 54, 58
- We can see none of the numbers are repeated.
Therefore, there is no mode for data set (a) as there is no number that repeats.
#### ii) Mean of data (a):
The mean is the sum of all data points divided by the number of data points.
- Sum of data points: 26 + 28 + 31 + 32 + 33 + 37 + 45 + 46 + 51 + 54 + 58
- Sum: 441
- Number of data points: 11
Mean = Total Sum / Number of Data Points = 441 / 11 = 40.09
### Data (b):
This data is also presented in a stem-and-leaf plot format. First, we need to list out the data points:
- Stem 3: Leaves 5 → Data points: 35
- Stem 4: Leaves 2, 7, 9 → Data points: 42, 47, 49
- Stem 5: Leaves 2, 2, 2, 3, 3, 6 → Data points: 52, 52, 52, 53, 53, 56
- Stem 6: Leaves 8 → Data points: 68
- Stem 7: Leaves 3, 4, 5, 8, 9 → Data points: 73, 74, 75, 78, 79
- Stem 8: Leaves 4, 4, 4, 7 → Data points: 84, 84, 84, 87
So, the complete data set for (b) is: 35, 42, 47, 49, 52, 52, 52, 53, 53, 56, 68, 73, 74, 75, 78, 79, 84, 84, 84, 87
#### i) Mode of data (b):
The mode is the value that appears most frequently in a data set.
- Checking the data set: 35, 42, 47, 49, 52, 52, 52, 53, 53, 56, 68, 73, 74, 75, 78, 79, 84, 84, 84, 87
- The number 52 appears 3 times, and the number 84 also appears 3 times. Both are the most frequent.
Therefore, the modes for data set (b) are 52 and 84 (bimodal).
#### ii) Mean of data (b):
The mean is the sum of all data points divided by the number of data points.
- Sum of data points: 35 + 42 + 47 + 49 + 52 + 52 + 52 + 53 + 53 + 56 + 68 + 73 + 74 + 75 + 78 + 79 + 84 + 84 + 84 + 87
- Sum: 1223
- Number of data points: 20
Mean = Total Sum / Number of Data Points = 1223 / 20 = 61.15
### Summary:
Data (a):
- Mode: No mode
- Mean: 40.09
Data (b):
- Mode: 52, 84 (bimodal)
- Mean: 61.15
