Solving Statistics Problem: Age Distribution of Promotion-Sensitive Shoppers

[zfolwick]

Homework Statement

What is the age distribution of promotion-sensitive shoppers? A supermarket super shopper is defined as a shopper for whom at least 70% of the items purchased were on sale or purchased with a coupon. The following table is based on information taken from Trends in the United States (Food Marketing Institute, Washington, D.C.).
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 8% 45% 23% 12% 12%
For the 62-and-over group, use the midpoint 67 years.

(d) Compute the standard deviation σ for ages of super shoppers. (Use 2 decimal places.)

Homework Equations

The expected age was correctly calculated to be 42.25 years

The Attempt at a Solution

Attempt 1:
6.5 was my first answer won't work


I tried the following in R:
x<-c(23,34,45,56,67)
percent<-c(.08,.45,.23,.12,.12)
sd(x)
[1] 17.39253

I also tried the following code:
stand<-sum((x-ave)^2*percent)
> stand
[1] 158.2075

which cannot possibly be correct.

Any ideas?

 

[lanedance]

in effect you have a discrete probability distribution, with probability pi for each point xi

the sample SD is given by:
$$s = \sqrt{ \sum_i p_i(x_i-\mu)^2}$$