Respuesta :
Answer:
Step-by-step explanation:
First we arrange these data into ascending order (least to greatest)
25, 28, 29, 30, 32, 33, 34, 34, 35, 35, 39, 40, 44, 49, 50,78
a) 5 number summary :
Minimum : 25
[tex]Q_{1}[/tex] = [tex]\frac{30+32}{2}[/tex] = 31 [median of first half of the data]
Median : [tex]\frac{34+35}{2}[/tex] = 34.5
[tex]Q_{3}[/tex] = [tex]\frac{40+44}{2}[/tex] = 42 [median of first half of the data]
Maximum : 78
For [tex]P_{30}[/tex] we have to use the formula [tex]\frac{30n}{100}[/tex]
where n = total number of the data
= [tex]\frac{30\times 16}{100}[/tex] = 4.8 ≈ 5
So [tex]P_{30}[/tex] = 5th term of the data = 32
Minimum : 25, [tex]Q_{1}[/tex] : 31 Median : 34.5, [tex]Q_{3}[/tex] : 42, Maximum : 78
b) Standard deviation :
Mean of the data : [tex]\frac{25+28+29+30+32+33+34+34+35+35+39+40+44+49+50+78}{16}[/tex] = 38.4
Now we will subtract mean and square the result.
25 = -13.4 = 179.56
28 = -10.4 = 108.16
29 = -9.4 = 88.36
30 = -8.4 = 70.56
32 = -6.4 = 40.96
33 = -5.4 = 29.16
34 = -4.4 = 19.36
34 = -4.4 = 19.36
35 = -3.4 = 11.56
35 = - 3.4 = 11.56
39 = 0.6 = 0.36
40 = 1.6 = 2.56
44 = 5.6 = 31.36
49 = 10.6 = 112.36
50 = 50.6 = 134.56
78 = 39.6 = 1568.16
Now take out mean of those results and find the square root.
[tex]\frac{179.56+108.16+88.36+70.56+40.96+29.16+19.36+19.36+11.56+11.56+0.36+2.56+31.36+112.36+134.56+1568.16}{16}[/tex]
= [tex]\frac{2428}{16}[/tex]
= 151.75
Now square the result [tex]\sqrt{151.75}[/tex] = 12.3186 ≈ 12.32
Range = Maximum - minimum
= 78 - 25 = 53
Interquartile Range (IQR) = [tex]Q_{3}- Q_{1}[/tex]
= 42 - 31 = 11
c) Outliers : The number of the given data there is a number which is far from the other numbers is called outliers that is 78
Outlier = 78
