MATH SOLVE

3 months ago

Q:
# The numbers of rooms for 15 homes recently sold were: 8, 8, 8, 5, 9, 8, 7, 6, 6, 7, 7, 7, 7, 9, 9. what is the sample standard deviation?

Accepted Solution

A:

From the data set given:

8, 8, 8, 5, 9, 8, 7, 6, 6, 7, 7, 7, 7, 9, 9

to get the standard deviation we use the formula for variance given by:

σ²=[Σ(x-μ)²]/(n-1)

σ² is the variance

μ is the mean

The mean of the data will be:

μ=(8+8+8+5+9+8+7+6+6+7+7+7+7+9+9)/15=7.4

The variance will be found as follows:

σ²=[(8-7.4)²×4+(5-7.4)²+3×(9-7.4)²+5×(7-7.4)²+2×(6-7.4)²]/(15-1)

σ²=1.4

thus

σ=√1.4=1.1183

8, 8, 8, 5, 9, 8, 7, 6, 6, 7, 7, 7, 7, 9, 9

to get the standard deviation we use the formula for variance given by:

σ²=[Σ(x-μ)²]/(n-1)

σ² is the variance

μ is the mean

The mean of the data will be:

μ=(8+8+8+5+9+8+7+6+6+7+7+7+7+9+9)/15=7.4

The variance will be found as follows:

σ²=[(8-7.4)²×4+(5-7.4)²+3×(9-7.4)²+5×(7-7.4)²+2×(6-7.4)²]/(15-1)

σ²=1.4

thus

σ=√1.4=1.1183