I have 33 whole number observation data set. The five number set from the box and whisker plot is 16, 20, 22, 30, 46). How many observations are strictly less than 22(answer should be a ra nge of numbers)?
Is it possible that there is no observation equal to 22? Explain briefly.
How many observations are strictly less than 20? (answer should be a range of numbers)
is it possible that there is no observation equal to 20?
how many observations are strictly less than 22? A:16
To determine the number of observations that are strictly less than 22, we need to consider the given five-number summary from the box and whisker plot. The numbers in the five-number summary are 16, 20, 22, 30, and 46. From this information, we know that there are observations at or below 16, at or below 20, at or below 22, at or below 30, and at or below 46.
To find the number of observations strictly less than 22, we need to subtract the number of observations up to and including 22 from the total number of observations. From the five-number summary, we know that there are observations up to and including 22, so we subtract that value from the total number of observations.
Given that there are 33 observations in total, we can calculate the number of observations strictly less than 22:
33 - (number of observations up to and including 22).
The number of observations up to and including 22 is the cumulative frequency of the class interval that contains 22, which we can determine using the given five-number summary. If we assume that the given five-number summary represents quartiles and a median, we can estimate the cumulative frequencies for each quartile.
Let's calculate the cumulative frequency for 22:
Cumulative frequency for 22 = (Number of observations up to and including 22) = (Number of observations up to and including 20) + the frequency of 22.
Without the frequency data, we cannot calculate the exact number of observations strictly less than 22, but we can provide a range of possible values.
Considering that the five-number summary is given without any frequencies, it is technically possible that there are no observations equal to 22. The five-number summary only provides information about the minimum, first quartile, median, third quartile, and maximum values in the dataset, but it does not provide any information about the frequencies of each value.
To determine the number of observations strictly less than 20, we follow the same process. Subtract the number of observations up to and including 20 from the total number of observations.
Given that there are 33 observations in total, we can calculate the number of observations strictly less than 20 using the cumulative frequency for 20. Again, without the frequency data, we cannot calculate the exact number of observations, but we can provide a range of possible values.
As with the previous question, it is possible that there are no observations equal to 20, as the five-number summary does not provide information about the frequencies of each value.