Question

Upgrade 1to macc Dark Mode, s Question 15 4,9, 16,5, 18, 17,30,22, 11,27,32, 15, 26, 22, 26 Using Statkey or other technology, find the following values for the above data. Click here to access Statkey (a) The mean and the standard deviation Round your answers to one decimal place. standard deviation- (b) The five number summary Enter exact answers. The five number summary is eTextbook and Media Attempts: u

Answer 1

Solution :

Given that 4,9,16,5,18,17,30,22,11,27,32,15,26,22,26

(a) => mean μ = 18.7

=> Mean = sum of terms/number of terms

= (4 + 9 + 16 + 5 + .... + 26)/15

= 280/15

= 18.6667

= 18.7 (rounded)

=>   standard deviation σ = 8.8 (rounded)

(b)
=> The five number summary is (4 , 11 , 18 , 26 , 32)

==> the minimum value from the data set is 4

==> the first quartile Q1 of the data set = 11

=> The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

4 5 9 11 15 16 17 18 22 22 26 26 27 30 32   

=> So, the bottom half is

4 5 9 11 15 16 17   

=> The median of these numbers is 11

=> the first quartile Q1 = 11

==> The median of the data set is 18

=> The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

4 5 9 11 15 16 17 18 22 22 26 26 27 30 32   

=> So, the median is 18

==> The third Quartile Q3 of the data set is 26

=> The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

4 5 9 11 15 16 17 18 22 22 26 26 27 30 32   

=> So, the upper half is

22 22 26 26 27 30 32   

=> The median of these numbers is 26.

=> Q3 = 26

==> The maximum value from the data set is 32