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:

  1. How is the standard deviation different from variance?
  2. What is the difference between population and sample standard deviation?
  3. How would the mean and standard deviation change if a new value was added to the data?
  4. How can the range of a data set give insights into variability?
  5. 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