High School

The five-number summary for a large sample of data is 33, 42, 47, 51, 76.

What percent of the data is expected to be within the interval 42 to 51?

A. 68%
B. 50%
C. 25%
D. 60%
E. 20%
F. 75%

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.

To know more about five-number summary visit:

https://brainly.com/question/30767783

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