Math Problem Statement
The table below gives the number of hours spent watching TV last week by a sample of 16 children. The values have been sorted. Find the minimum, maximum, range, mean, and standard deviation of the following data using StatCrunch, Excel, a calculator or other technology. The minimum, maximum, range should be entered as exact values. Round the mean and standard deviation to two decimals places. x 10 11 12 17 20 28 29 32 35 37 39 40 42 45 48 50
Min = Max = Range = Mean = Standard Deviation =
Solution
Here are the calculated values:
- Minimum = 10
- Maximum = 50
- Range = 40
- Mean = 30.94
- Standard Deviation = 12.98
Would you like more details on how these were calculated, or do you have any further questions?
Here are five related questions:
- How is the standard deviation different from variance?
- What is the difference between population and sample standard deviation?
- How would the mean and standard deviation change if a new value was added to the data?
- How can the range of a data set give insights into variability?
- Why is it important to sort data before performing statistical analysis?
Tip: When interpreting standard deviation, a lower value indicates that data points are closer to the mean, while a higher value suggests more spread-out data.
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Math Problem Analysis
Mathematical Concepts
Statistics
Descriptive Statistics
Formulas
Minimum = smallest value in the data set
Maximum = largest value in the data set
Range = Maximum - Minimum
Mean = (Sum of all values) / (Number of values)
Standard Deviation = sqrt((Σ(x - mean)^2) / (n - 1))
Theorems
Measures of Central Tendency
Measures of Spread
Suitable Grade Level
Grades 9-12
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