Find five rational numbers between ? explain please
1 answer:
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Answer:
(a) The mean is 65.9, the median is, 66.5 and the mode is. 61.
(b) The first and third quartiles are 61 and 71 respectively.
(c) The value of the 90th percentile is, 78.3.
Step-by-step explanation:
The ratings of 20 top-of-the line jackets, arranged in ascending order are as follows:
S = {42 , 53 , 54 , 61 , 61 , 61 , 62 , 63 , 64 , 66 , 67 , 67 , 68 , 69 , 71 , 71 , 76 , 78 , 81 , 83}
(a)
Compute the mean as follows:
Compute the median as follows:
For an even number of values the median is the average of the middle two values.
Compute the mode as follows:
The mode of a dataset is the term that occurs most of the time.
Thus, the mean is 65.9, the median is, 66.5 and the mode is. 61.
(b)
The first quartile is the median of the first half of the data set.
S₁ = {42 , 53 , 54 , 61 , 61 , 61 , 62 , 63 , 64 , 66}
The third quartile is the median of the second half of the data set.
S₂ = {67 , 67 , 68 , 69 , 71 , 71 , 76 , 78 , 81 , 83}
Thus, the first and third quartiles are 61 and 71 respectively.
(c)
The <em>p</em>th percentile is a data value such that at least p% of the data set is less-than or equal to this data value and at least (100 - p)% of the data-set are more-than or equal to this data value.
Use the Excel formula "=PERCENTILE.INC(array,0.9)" to compute the 90th percentile.
The value of the 90th percentile is, 78.3.
This value implies that 90% of the ratings are less than 78.3.
Answer:
The measure of the angle ACB is 59°.
Step-by-step explanation:
Let be the location of the center of circle and
is the radius of the figure, the triangles ACD and BCD are isosceles triangles, since
. And the measure of the angle C associated with each triangle are, respectively:
Triangle ACD
Triangle BCD
Lastly, the measure of the angle ACB is:
The measure of the angle ACB is 59°.