Open Class Interval Problem from AS S1

In summary, the conversation is about calculating the mean and standard deviation for a set of data represented in a table. The question involves finding the appropriate mid-values for four intervals in three different cases. The first two cases are considered okay, but there is a problem with the third case, as it is unclear what type of variable is being measured. After some discussion, the variable is determined to be discrete and the appropriate mid-values are listed as 15, 25, 35, and 45.5.
  • #1
Micky76
4
0

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 :).
 
Physics news on Phys.org
  • #2
Problem solved.
 

Related to Open Class Interval Problem from AS S1

1. What is an open class interval?

An open class interval is a type of interval in statistics that includes all values between two numbers, but does not include the endpoints. For example, an open class interval from 10 to 20 would include all values greater than 10 and less than 20, but not including 10 and 20.

2. Why is the open class interval problem important in AS S1?

The open class interval problem is important in AS S1 because it allows us to accurately analyze and interpret data. By using open class intervals, we can avoid overestimating or underestimating the frequency of data values and make more precise calculations and predictions.

3. How do you calculate the width of an open class interval?

The width of an open class interval is calculated by subtracting the lower limit from the upper limit. For example, if the upper limit is 20 and the lower limit is 10, the width would be 20-10=10.

4. Can you have multiple open class intervals in one data set?

Yes, it is possible to have multiple open class intervals in one data set. This can happen when there is a large range of data values and using only one open class interval would not accurately represent the frequency of the data.

5. How does the number of open class intervals affect the accuracy of the data analysis?

The number of open class intervals can greatly affect the accuracy of the data analysis. If there are too few open class intervals, the data may be oversimplified and important patterns or trends may be missed. On the other hand, if there are too many open class intervals, the data may be too complex and difficult to interpret. It is important to choose an appropriate number of open class intervals to accurately represent the data.

Similar threads

  • Programming and Computer Science
Replies
2
Views
406
  • Precalculus Mathematics Homework Help
Replies
12
Views
2K
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
14
Views
2K
  • Calculus and Beyond Homework Help
Replies
4
Views
1K
  • Nuclear Engineering
Replies
1
Views
3K
  • Set Theory, Logic, Probability, Statistics
Replies
6
Views
2K
  • Calculus and Beyond Homework Help
Replies
7
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
1K
Back
Top