Asked by Kevin
Name: ___________________________________________________
In 7–11, use the data to answer the questions.
Lengths of Long Jumps in Mr. Hansen’s
Physical Education Class (in inches)
All Answers 1
Answered by
GPT-5 mini
AI
I don't see the actual data or the specific questions 7–11. Could you paste the list of jump lengths and the questions? I can then solve them step by step.
Meanwhile, here is a quick guide to the common tasks for a data set of long jump lengths, plus a worked example so you see how I would answer 7–11 once you provide the real data.
Common computations you might be asked for:
- Mean (average): sum of values divided by count.
- Median: middle value (or average of two middle values) after sorting.
- Mode: most frequent value(s).
- Range: max − min.
- Q1, Q3, IQR: quartiles and interquartile range; used to find outliers (1.5·IQR rule).
- Standard deviation (sample or population): measure of spread.
- Create frequency table, histogram, boxplot, or stem-and-leaf plot.
- Interpret whether there are outliers or whether the distribution is skewed.
Worked example
Suppose the measured jump lengths (in inches) are:
54, 55, 56, 57, 58, 58, 59, 60, 60, 61, 62, 62, 63, 64, 65, 66, 67, 68, 69, 70
1) Mean:
Sum = 1,234; count = 20 ⇒ mean = 1,234 / 20 = 61.7 inches
2) Median:
Sorted list shown above. Middle two values (10th and 11th) are 61 and 62 ⇒ median = (61 + 62)/2 = 61.5 inches
3) Mode:
58, 60, and 62 each occur twice ⇒ multimodal: 58, 60, 62
4) Range:
70 − 54 = 16 inches
5) Quartiles and IQR:
Lower half (first 10): median of that = Q1 = 58
Upper half (last 10): median of that = Q3 = 65.5
IQR = 65.5 − 58 = 7.5
6) Outlier check (1.5·IQR rule):
1.5·IQR = 11.25
Lower fence = Q1 − 11.25 = 46.75
Upper fence = Q3 + 11.25 = 76.75
No data below 46.75 or above 76.75 ⇒ no outliers
7) Standard deviation:
Sum of squared deviations ≈ 426.20
Population variance = 426.20 / 20 = 21.31 ⇒ population SD ≈ 4.62
Sample variance = 426.20 / 19 ≈ 22.43 ⇒ sample SD ≈ 4.74
If you paste the actual jump lengths and the precise questions 7–11, I will compute the exact answers for your worksheet.
Meanwhile, here is a quick guide to the common tasks for a data set of long jump lengths, plus a worked example so you see how I would answer 7–11 once you provide the real data.
Common computations you might be asked for:
- Mean (average): sum of values divided by count.
- Median: middle value (or average of two middle values) after sorting.
- Mode: most frequent value(s).
- Range: max − min.
- Q1, Q3, IQR: quartiles and interquartile range; used to find outliers (1.5·IQR rule).
- Standard deviation (sample or population): measure of spread.
- Create frequency table, histogram, boxplot, or stem-and-leaf plot.
- Interpret whether there are outliers or whether the distribution is skewed.
Worked example
Suppose the measured jump lengths (in inches) are:
54, 55, 56, 57, 58, 58, 59, 60, 60, 61, 62, 62, 63, 64, 65, 66, 67, 68, 69, 70
1) Mean:
Sum = 1,234; count = 20 ⇒ mean = 1,234 / 20 = 61.7 inches
2) Median:
Sorted list shown above. Middle two values (10th and 11th) are 61 and 62 ⇒ median = (61 + 62)/2 = 61.5 inches
3) Mode:
58, 60, and 62 each occur twice ⇒ multimodal: 58, 60, 62
4) Range:
70 − 54 = 16 inches
5) Quartiles and IQR:
Lower half (first 10): median of that = Q1 = 58
Upper half (last 10): median of that = Q3 = 65.5
IQR = 65.5 − 58 = 7.5
6) Outlier check (1.5·IQR rule):
1.5·IQR = 11.25
Lower fence = Q1 − 11.25 = 46.75
Upper fence = Q3 + 11.25 = 76.75
No data below 46.75 or above 76.75 ⇒ no outliers
7) Standard deviation:
Sum of squared deviations ≈ 426.20
Population variance = 426.20 / 20 = 21.31 ⇒ population SD ≈ 4.62
Sample variance = 426.20 / 19 ≈ 22.43 ⇒ sample SD ≈ 4.74
If you paste the actual jump lengths and the precise questions 7–11, I will compute the exact answers for your worksheet.
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