Open Class Interval Problem from AS S1

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SUMMARY

The discussion centers on the Open Class Interval Problem, specifically addressing the calculation of mid-values for different types of random variables. Anna successfully calculates mid-values for continuous and discrete variables, yielding results of 15, 25, 35, 45 for weight and 14.5, 24.5, 34.5, 45 for misprints. However, confusion arises regarding the age variable, where the correct mid-value is 15, 25, 35, and 45.5, highlighting the distinction between discrete and continuous variables in statistical analysis.

PREREQUISITES
  • Understanding of continuous and discrete random variables
  • Familiarity with calculating mid-values in frequency distributions
  • Knowledge of statistical measures such as mean and standard deviation
  • Basic grasp of interval notation in statistics
NEXT STEPS
  • Study the differences between continuous and discrete variables in statistics
  • Learn how to calculate mid-values for various types of data distributions
  • Explore the implications of using open class intervals in statistical analysis
  • Review statistical measures including mean, median, and standard deviation calculations
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Students preparing for statistics exams, educators teaching statistical concepts, and anyone interested in understanding the classification of random variables and their implications in data analysis.

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Homework Statement


Question

Anna is calculating the mean and standard deviation for a set of data for a random
variable X. The data is summarised in the table below.

x: 10– 20– 30– 40–50
Frequency: 8 20 12 0

(i) For each of the following cases, write down the appropriate mid-values of the four
intervals.

(a) X is the weight of a letter, in grams. (This one is okay, variable is continuous)
(b) X is the number of misprints in a magazine. (This one is okay, variable discrete)
(c) X is the age, in complete years, of the audience at a cinema. (Problem)

Answers:
(a) 15, 25, 35, 45
(b) 14.5, 24.5, 34.5, 45
(c) 15, 25, 35, 45.5 (3 s.f.)

Homework Equations



The Attempt at a Solution


I understand a) and b) fine. However, I can't figure out c) since I can't figure out what type of variable it is. I initially thought it would be discrete, due to the number of *complete* years. Would that not make the answer the same as that to b) though?
Any clarification is greatly appreciated, exams coming soon :).
 
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Problem solved.
 

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