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Answer :
25% of the data is expected to be within the interval 42 to 51.
The five-number summary for a large sample of data was found to be 33,42,47,51, 76.
What percent of the data is expected to be within the interval 42 to 51 is 25%.
What is the five-number summary?
In statistics, a five-number summary is a collection of descriptive statistics. Minimum and maximum values are included in the five-number summary, as well as the first (Q1) and third (Q3) quartiles and the median.
It gives a general overview of the data in a concise way.
What is the interquartile range?
The interquartile range (IQR) is the distance between the first quartile (Q1) and the third quartile (Q3) of a dataset. The IQR gives the range of the middle 50% of the data (the range of data between the 25th and 75th percentiles).
Solution: Given that, the five-number summary for a large sample of data was found to be 33,42,47,51, 76.
Here, Q1 = 42, Q3 = 51
The data that lies between Q1 and Q3 is known as Interquartile range (IQR)IQR = Q3 - Q1= 51 - 42= 9
To calculate the percentage of data between 42 and 51:
So, data within 42 and 51 can be written as Q1 - IQR/2 to Q3 + IQR/2
= 42 - 9/2 to 51 + 9/2
= 37.5 to 55.5
Therefore, 25% of the data is expected to be within the interval 42 to 51.
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