1. To create a stem and leaf plot for the ages of teachers at Drew High School, we first separate each age into a stem (the tens digit) and a leaf (the ones digit). The data is: 27, 45, 56, 31, 29, 36, 42, 50, 43, 61, 59, 48, 36, 23.
- Stem 2: 7, 9, 3
- Stem 3: 1, 6, 6
- Stem 4: 5, 2, 3, 8
- Stem 5: 6, 0, 9
- Stem 6: 1
The stem and leaf plot is:
```
Stem | Leaf
2 | 7 9 3
3 | 1 6 6
4 | 5 2 3 8
5 | 6 0 9
6 | 1
```
2. To create a stem and leaf plot for the horizontal jump distances, we separate each measurement into a stem (the whole number) and a leaf (the decimal part). The data is: 3.5, 4.8, 2.1, 5.6, 4.3, 3.9, 6.0, 5.9, 2.7, 4.9, 5.8, 3.5.
- Stem 2: 1, 7
- Stem 3: 5, 9, 5
- Stem 4: 8, 3, 9
- Stem 5: 6, 9, 8
- Stem 6: 0
The stem and leaf plot is:
```
Stem | Leaf
2 | 1 7
3 | 5 9 5
4 | 8 3 9
5 | 6 9 8
6 | 0
```
3. The mean of the scores is calculated by summing all the scores and dividing by the number of scores. The scores are: 35, 45, 55, 66, 68, 71, 73, 74, 78, 78, 78, 79, 80, 82, 86, 86, 91, 93, 94, 99, 100, 100.
Sum = 35 + 45 + 55 + 66 + 68 + 71 + 73 + 74 + 78 + 78 + 78 + 79 + 80 + 82 + 86 + 86 + 91 + 93 + 94 + 99 + 100 + 100 = 1540
Number of scores = 21
Mean = 1540 / 21 ≈ 73.33
4. The mode is the score that appears most frequently. Looking at the stem and leaf plot, the stem 7 has the highest frequency with 5 scores (71, 73, 74, 78, 78, 78, 79). The score 78 appears 3 times, which is more than any other score. So, the mode is 78.
5. An outlier is a data point that is significantly different from the others. In this case, 35 is much lower than the rest of the scores, and 100 is much higher. However, 35 is the only one that is significantly lower. So, 35 is an outlier.
6. The percentage of the class that passed the test (70+) is calculated by counting the number of scores 70 or higher and dividing by the total number of scores. The scores 70 or higher are: 71, 73, 74, 78, 78, 78, 79, 80, 82, 86, 86, 91, 93, 94, 99, 100, 100. There are 16 scores.
Percentage = (16 / 21) * 100 ≈ 76.19%
7. The range is the difference between the highest and lowest scores. The highest score is 100, and the lowest score is 35.
Range = 100 - 35 = 65
8. The median score is the middle value when the scores are arranged in order. There are 21 scores, so the median is the 11th score. Arranging the scores: 35, 45, 55, 66, 68, 71, 73, 74, 78, 78, 78, 79, 80, 82, 86, 86, 91, 93, 94, 99, 100, 100. The 11th score is 78.
Median = 78
9. The stem with the highest frequency is the one with the most leaves. Looking at the stem and leaf plot, stem 7 has 5 leaves (71, 73, 74, 78, 78, 78, 79), which is more than any other stem.
Stem 7 has the highest frequency.
10. The scores are not evenly distributed because there is a cluster of scores around the 70s and 80s, and a few scores at the lower and higher ends. The distribution is skewed to the left due to the outlier at 35.
Parent Tip: Review the logic above to help your child master the concept of stem and leaf plot worksheets.
