Respuesta :
Answer:
Mean = 47
Median = 47.38
Standard Deviation = 12.73
Explanation:
Note: You wrote " 40 manufacturing companies, but the total number of companies you actually listed is 75, definitely you meant 75.
Let y represent the range of advertising expenditure, f represent the number of companies, x represent the midpoint of the range of advertising expenditure.
y f x fx fx²
$20 to under $30 9 25 225 5625
$30 to under $40 13 35 455 15925
$40 to under $50 21 45 945 42525
$50 to under $60 18 55 990 54450
$60 to under $70 14 65 910 59150
n = 75 [tex]\sum fx = 3525[/tex]
[tex]\sum fx^2 = 177675[/tex]
Mean, [tex]\bar{X} = \frac{\sum fx}{n}[/tex]
[tex]\bar{X} = \frac{3525}{75} \\\bar{X} = 47[/tex]
Standard Deviation:
[tex]SD = \sqrt{\frac{n \sum fx^2 - (\sum fx)^2}{n(n-1)} } \\SD = \sqrt{\frac{(75*177675) - (3525)^2}{75(75-1)} }\\SD = 12.73[/tex]
Median:
Get the cumulative frequencies(cf)
y f cf
$20 to under $30 9 9
$30 to under $40 13 22
$40 to under $50 21 43
$50 to under $60 18 61
$60 to under $70 14 75
N = 75
Median = Size of (N/2)th item
Median = Size of (75/2)th item
Median = Size of (37.5)th item
The median class = 40 to under 50
Lower limit, L₁ = 40
Cumulative frequency, cf = 22
f = 21
Class Width, h = 10
Median = [tex]L_1 + \frac{ (N/2) - cf}{f} * h\\[/tex]
Median = [tex]40 + \frac{ (75/2) - 22}{21} * 10\\[/tex]
Median = 47.38
