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Age range, years 18-28 29-39 40-50 51-61 62 and over
Midpoint x 23 34 45 56 67
Percent of super shoppers 9% 46% 22% 11% 12%
For the 62-and-over group, use the midpoint 67 years.
(a) Compute the expected age μ of a super shopper. (Round your answer to two decimal places.)
μ = yr
(b) Compute the standard deviation σ for ages of super shoppers. (Round your answer to two decimal places.)
σ = yr

Sagot :

Fichohidn

Answer:

41.81 ; 12.67

Step-by-step explanation:

Given the data:

Age range, years 18-28 29-39 40-50 51-61 62 and over

Midpoint x 23 34 45 56 67

Percent of super shoppers 9% 46% 22% 11% 12%

Midpoint, x : 23 34 45 56 67

Frequency, f : 0.09_ 0.46 _ 0.22 __0.11 __ 0.12

The mean(m)

Σfx / Σf

[(23 * 0.09) + (34 * 0.46) + (45 * 0.22) + (56 * 0.11) + (67 * 0.12)] / (0.09 + 0.46 + 0.22 + 0.11 + 0.12)

= 41.81 / 1

Mean = 41.81

Standard deviation :

Sqrt[(Σ(X² * f) / Σf) - m²)]

((23^2*0.09) + (34^2*0.46) + (45^2*0.22) + (56^2*0.11) + (67^2*0.12)) / 1

1908.51 - 41.81^2

Sqrt(160.4339)

= 12.666250

= 12.67

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