Respuesta :
Answer:
The question is not complete because we were not given the data that represent the miles per gallon of a random sample of smart cars with a three cylinder, 1.0-liter engine.
However, we are going to assume some data below such that whatever data is latter provided, the solution to the question follows the sama procedure and pattern.
Sample Data = 31.5, 36.0, 37.8, 38.5, 40.1, 42.2, 34.2, 36.2, 38.1, 38.7, 40.6, 42.5, 34.7, 37.3, 38.2, 39.5, 41.4, 43.4, 35.6, 37.6, 38.4, 39.6, 41.7, 49.3
Now to solve for
(a) which is to compute the Z-score corresponding to the individual who obtained 37.837.8 miles per gallon.
Therefore, the value of z-score is calculated as follows,
μ = Σ lin (n) lin (i=1) X₁ / n → 933.1 /24 → 38.88
σ = √ Σ lin (n) lin (i=1) X₁² - nX⁻²/ n - 1 → 3.61
z = X - μ / σ → 37.8 - 38.88/3.61 = − 0.299
Therefore, the value of z-score is -0.299.
(b) Considering the fact that the values are in ascending order is given as,
Recalling the values: 31.5, 36, 37.8 ,38.5, 40.1 ,42.2, 34.2 ,36.2, 38.1, 38.7, 40.6 ,42.5, 34.7, 37.3 ,38.2, 39.5 ,41.4, 43.4, 35.6, 37.6 ,38.4 ,39.6 ,41.7, 49.3
Q₁ = ( n+1/4)th value → (24+1/4)th value → 6.25th value → 36.2 + 0.25 ∗ ( 37.3 − 36.2 ) => 36.47
M = ( n+1/2)th value → (24+1/2)th value = (24+1/4)th value => 12.5 t h v a l u e => 38.4 + 38.5/2 = 38.45
Q₃ = 3( n+1/4)th value → 3(24+1/4)th value => 18.75 t h v a l u e => 40.6 + 0.75 ∗ ( 41.4 − 40.6 ) => 41.2
(c) I n t e r q u a r t i l e r a n g e = Q ₃ − Q ₁ => 41.2 − 36.47 => 4.25
Therefore, the IQR value is measure of spread of data, and here the value of IQR = 4.25.
(d) L o w e r f o u r t h = Q₁− 1.5 ( I Q R ) => 36.75 − 1.5 ( 4.25 ) => 30.375 U p p e r f o u r t h = Q ₃ + 1.5 ( I Q R ) => 41 + 1.5 ( 4.25 ) => 47.375
Hence, there is outliers since observations are not less than 30.375 and greater than 47.375.
The table for the entire problem is given as,
Z- Score -0.299
Q₁ 36.47
Q₂ 38.45
Q₃ 41.2
IQR 4.25
Lower fourth 30.375
Upper fourth 47.375
