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?

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