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If I have a market research with population of 100 individuals:

  1. 10 spend less than 10 dollars in clothing
  2. 20 spend between 10 - 20 dollars in clothing
  3. 30 spend between 20 - 100 dollars in clothing
  4. the remaining do not spend at clothing.

How do I calculate to arithmetic average and standard deviation of the data?

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You cannot calculate these without further assumptions.

The simplest would be to assume that spending in each bin is uniformly distributed.

Then the mean is easy: Since the 10 people under \$10 are uniformly distributed, it's just as if all 10 spent \$5 (halfway between \$0.01 and \$9.99). Similarly, 20 spent \$15 and 30 spent \$60. \$100 + \$300 + \$1800 = \$2200 and there were 100 people so that's \$22 per person.

For the standard deviation, it's probably easiest to simulate the data

set.seed(1020101)
a <- runif(10, 0, 9.99)
b <- runif(20, 10, 19.99)
c <- runif(30, 20, 99.99)
d <- rep(0, 60)
total <- c(a,b,c,d)
sd(total)

and run it several times.

Alternatively, see Dr. Math

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