Statistics 1

Listed below are the commissions earned ($000) last year by the sales representatives at the Furniture Patch, Inc.

4.4 6.3 7.7 11.1 12.1 13.6 15.3 15.8 16.7 17.4 18.1 22.3 36.6 43.2 83.9

(a) (Round your answers to 2 decimal places.)

The mean is _______ thousand

The median is ________ thousand

The standard deviation is ________ thousand

Solution: Mean (average) = 21.63 thousand

Median (middle value) = 15.8 thousand

Standard Deviation = sqrt ( Σ (X - M)² / n - 1 )

where Σ = Sum of

X = Individual score

M = Mean of all scores

N = Sample size (Number of scores)

To find the Standard deviation of 4.4, 6.3, 7.7, 11.1, 12.1, 13.6, 15.3, 15.8, 16.7, 17.4, 18.1, 22.3, 36.6, 43.2, and 83.9

Step 1: Calculate the mean and deviation.

Step 2:Find the sum of (X-M)²

= 5688.16

Step 3: N = 15, the total number of values. Find N-1

15-1 = 14

Step 4:Now find Standard Deviation using the formula

sqrt (5688.16 / 14 )

= sqrt 406.3

= 20.16 thousand

(b)Determine the coefficient of skewness using Pearsons method. (Round your answer to 3 decimal places.)

Solution: Coefficient of Skewness = 3 * [( mean - median) / standard deviation ]

The coefficient is usually positive when the distribution is positively skewed, and negative when it is negatively skewed.

Coefficient of Skewness = 3 * ( 21.63 – 15.8) / 20.16 = 0.8675 = 0.867