Respuesta :
The five-number summary for the given set of sample data is
1. Minimum value = 6
2. Lower quartile Q1 = 35
3. Median = 52
4. Upper quartile Q3 = 75
5. Maximum value = 100
How do calculate the five-number summary (min, Q1, median, Q3, max) for a given sample data?
The formulas for finding a five-number summary of a given set of n data values are:
Minimum value = least value from the entire data set
Maximum value = highest value from the entire data set
Lower quartile Q1 = 1/4 (n + 1)th term
Upper quartile Q3 = 3/4 (n + 1)th term
Median = middle term of the data set.
To find the median:
- Arrange the given data in the ascending order
- If the n value is odd then the median lies at (n+1)/2 th term
- If the n value is even then the median lies in between the two data values obtained by n/2 th term and the (n/2 + 1) th term.
Calculation:
The given set of sample data is
{6, 20, 24, 25, 26, 35, 40, 41, 43, 48, 50, 52, 53, 59, 66, 71, 72, 75, 79, 80, 83, 89, 100}
So, the sample size n = 23
The data is arranged in ascending order as
{6, 20, 24, 25, 26, 35, 40, 41, 43, 48, 50, 52, 53, 59, 66, 71, 72, 75, 79, 80, 83, 89, 100}
Then,
Minimum value = 6
Maximum value = 100
Calculating the median:
Since n = 23 is an odd number then the median lies at (n + 1)/2 th term
So,
Median = (23 + 1)/2 = 24/2 = 12th term
In th given set of data values, the 12th term is 52
∴ Median = 52
Calculating the lower quartile Q1:
Lower quartile Q1 = 1/4 (n + 1)th term
⇒ Q1 = 1/4(23 + 1)th term
⇒ Q1 = 1/4 × 24 = 6th term
From the given data set, the 6th term is 35
∴ Q1 = 35
Calculating the upper quartile Q3:
Upper quartile Q3 = 3/4(n + 1)th term
⇒ Q3 = 3/4(23 + 1)th term
⇒ Q3 = 3/4 × 24 = 18th term
From the given data set 18th term is 75
∴ Q3 = 75
Then the five-number summary for the given data set is {min = 6; Q1 = 35; median = 52; Q3 = 75; max = 100}
Learn more about the five-number summary(measures of dispersion) here:
https://brainly.com/question/17110151
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