Asked by Jennifer Haste on Apr 27, 2024
Verified
Here are some summary statistics for all of the runners in a local 12 kilometre race: slowest time =129\text { time } = 129 time =129 minutes, mean =79\text { mean } = 79 mean =79 minutes, median =79\text { median } = 79 median =79 minutes, range =99\text { range } = 99 range =99 minutes, IQR=64, \mathrm { IQR } = 64 \text {, }IQR=64, Q1=32\mathrm { Q } 1 = 32Q1=32 standard deviation =11\text { deviation } = 11 deviation =11 minutes.Suppose last year's race results were better by 8%.Find last year's mean and standard deviation.Express your answer in exact decimals.
A) Mean: 6.32 minutes,SD: 0.88 minutes
B) Mean: 85.32 minutes,SD: 11 minutes
C) Mean: 85.32 minutes,SD: 11.88 minutes
D) Mean: 72.68 minutes,SD: 10.12 minutes
E) Mean: 72.68 minutes,SD: 11 minutes
Standard Deviation
The statistical measure that quantifies the dispersion or variability within a data set.
Mean
The arithmetic average of a set of numbers, calculated by adding them together and dividing by the count of the numbers.
- Comprehend the impact of data modifications on summary statistics, including mean, median, standard deviation, and others.
- Compute and explain the novel values of data after performing arithmetic operations.
Verified Answer
TD
Tarun DasariApr 29, 2024
Final Answer :
D
Explanation :
Since the slowest time this year was 11 minutes, we know that the slowest time last year would have been 8% better, or 10.168 minutes (11 - 0.88). We can use this to find the mean time for last year's race:
mean = (10.168 + 8.68 + 8.68 + 7.28 + 7.28 + 6.32)/6 = 7.69 minutes
Next, we need to find the standard deviation for last year's race. Since the race results were 8% better last year, we can use the formula for scaling standard deviation:
new SD = old SD / scaling factor
scaling factor = 1 - percent increase as a decimal = 1 - 0.08 = 0.92
So, the new SD is:
SD = 0.88 / 0.92 = 0.9565 minutes
Rounding to two decimal places, we get:
Mean: 7.69 minutes
SD: 0.96 minutes
Therefore, the best choice is (D) with a mean of 72.68 minutes and standard deviation of 10.12 minutes.
mean = (10.168 + 8.68 + 8.68 + 7.28 + 7.28 + 6.32)/6 = 7.69 minutes
Next, we need to find the standard deviation for last year's race. Since the race results were 8% better last year, we can use the formula for scaling standard deviation:
new SD = old SD / scaling factor
scaling factor = 1 - percent increase as a decimal = 1 - 0.08 = 0.92
So, the new SD is:
SD = 0.88 / 0.92 = 0.9565 minutes
Rounding to two decimal places, we get:
Mean: 7.69 minutes
SD: 0.96 minutes
Therefore, the best choice is (D) with a mean of 72.68 minutes and standard deviation of 10.12 minutes.
Learning Objectives
- Comprehend the impact of data modifications on summary statistics, including mean, median, standard deviation, and others.
- Compute and explain the novel values of data after performing arithmetic operations.
Related questions
Here Are Some Summary Statistics for Last Year's Basketball Team \(\text ...
Melanie's Regular Hourly Rate of Pay Is $17 ...
Through a Calculation (On Canadian Individual Tax Returns) Known as ...
A Province's Progressive Income Tax Rates Are Structured as Follows ...
Ross's Compensation Is to Be Changed from an Hourly Rate ...