Answer to Question #218359 in Statistics and Probability for Leah

Question

The table below indicates the amounts paid by cars for parking at Anabel parking lot for a week. Use the information below to answer the questions that follow.
Amount paid ($)|200|250| 300| 350| 400| 450| 500| 550|
Number of cars|11| 8| 15| 20| 6| 10| 3| 12|

i) Estimate the mean amount paid
ii) Calculate the population standard deviation and interpret
iii) Estimate the skewness for the distribution and interpret

Answer 1

i)

Mean

$\bar{x}= \frac{\sum f(x) \times x}{\sum f(x)} \\ = \frac{30700}{85} \\ =361.17$

ii)

Population SD

$\sigma = \sqrt{ \frac{(\sum f(x) \times x^2) - \frac{(\sum f(x) \times x)^2}{n} }{n} } \\ \sqrt{ \frac{12105000 - \frac{(30700)^2}{85} }{85} } \\ = \sqrt{11963.3218} \\ = 109.3776$

Population standard deviation is $109.37. There is about $109.37 deviate the amount from mean value.

iii)

Population skewness

$SK = \frac{\sum (x_i - \bar{x})^3}{n \times \sigma^3} \\ = \frac{35680604.53}{85 \times (109.37)^3} \\ = 0.320$

Since SK>0 the distribution slightly negatively skewed.