Respuesta :
Answer:
The range of the data = 99 -22 = 77min
The mean of the dataset is given as
The IQR = 92 - 77 = 15 min
SIQR = IQR / 2 = 15 / 2 = 7.5 min
variance = 55.05 min
Step-by-step explanation:
First we need to arrange the data in ascending or descending order
22 ,58, 77, 84, 87, 87,91, 92, 99, 99 in ascending order
The range of the data is calculated by substracting the numbers at the extreme that is the lowest number subtracted from the highest number
range = 99 - 22 = 77min
The IQR stands for Inter-quartile range Q3 - Q1 where
Q1 is the middle value in the first half of the data set. i.e
Q1 is the middle of 22 ,58, 77, 84, 87 which is 77
Q1 = 77 min
Q3 is the middle value in the second half of the data set. i.e
Q3 is the middle of 87,91, 92, 99, 99 which is 92
Q1 = 92 min
Therefore IQR = Q3 - Q1 = 92min - 77min = 15 min
The SIQR stands for the semi-interquartile range. it is calculated by IQR / 2
SIQR = 15 / 2 = 7.5 min
To calculate the population variance we need to get the mean say X
The mean is the data point at the center. Since the dataset is even, there are two of them. which is 87 and 87
Therefore the mean is X = (87 + 87)/ 2 = 87
The variance = ∑[tex](X-x)^{2} /n[/tex]
where X is the mean = 87
x is a datapoint on the given dataset
n is the datasize = 10
variance = [tex]((22-87)^{2} + (58-87)^{2} + (77-87)^{2} + (84-87)^{2} + (87-87)^{2} + (87-87)^{2} + (91-87)^{2} + (92-87)^{2} + (99-87)^{2} + (99-87)^{2} ) /10[/tex]
variance = [tex]((-65)^{2} + (-29)^{2} + (-10)^{2} + (-3)^{2} + (0)^{2} + (0)^{2} + (4)^{2} + (5)^{2} + (12)^{2} + (12)^{2} ) /10[/tex]
variance = [tex]((4225) + (841) + (100) + (9) + (0) + (0) + (16) + (25) + (144) + (144) ) /10[/tex]
variance = 5505/10
variance = 550.5 min
Answer:
Range =77
IQR=15
SIQR=7.5
Variance=550.5
Step-by-step explanation:
Range:
First find the lowest and the highest number in the data and then subtract high with the low to find the range. 99-22=77.
IQR:
Ascend the data from low to high like this:
22 58 77 84 87 87 91 92 99 99
Then break into two half
22 58 77 84 87 | 87 91 92 99 99
Find the median of all the two half
77 is rhe median in the first half and 92 is the median in the second half.
Then subtract them: 92-77=15 IQR
SIQR:
Divide the IQR/2
Hence 15/2=7.5.
Variance:
Find the mean of the data first i.e. 79.6
variance = 5505/10
variance = 550.5
