5 exercises · 5 automatically checked · Untimed
5 questions · Shuffled order · Untimed practice
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A data set has value 1 occurring twice, value 2 occurring three times, and value 4 occurring five times. What is its mean?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 2.8
The weighted sum is 1(2) + 2(3) + 4(5)
Review worked example 3.03.
Review lesson: One-variable data: distributions, center, and spread
A data set has mean 10 and standard deviation 4. Subtract 6 from every value. What are the new mean and standard deviation?
Answer: D: mean 4; standard deviation 4
The mean shifts down by 6, from 10 to 4. Every value and the mean shift together, so deviations from the mean are unchanged; the standard deviation stays 4. A standard deviation cannot be negative.
Review worked example 3.10.
Review lesson: One-variable data: distributions, center, and spread
Seven numbers have mean 14. An eighth number is added, raising the mean to 15. What is the added number?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 22
The old total is 7(14)
Review worked example 3.08.
Review lesson: One-variable data: distributions, center, and spread
What is the median of 2, 5, 9, 12, 18, 21?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 10.5
The six values are already ordered. Average positions 3 and 4: (9 + 12)/2
Review worked example 3.02.
Review lesson: One-variable data: distributions, center, and spread
Data set A is 1, 4, 4, 4, 7 and B is 1, 1, 4, 7, 7. Which has the greater standard deviation?
Answer: B
Both means are 4. A has two observations 3 units from the mean; B has four. Their squared-deviation sums are 18 and 36, respectively. With equal data counts and a consistent convention, B has greater standard deviation.
Review worked example 3.12.
Review lesson: One-variable data: distributions, center, and spread
Review One-variable data: distributions, center, and spread