# Statistical formulas and algebraic demand analysis.

Here are some basic demand curve questions I'd like to verify with my solutions.

1

The number of deliveries per week for a sample of six customers.

3 4 5 6 2 4

A. Calculate the mean, median, and mode measures of central tendency for the number of deliveries per week.

Which measure does the best job of describing central tendency for this variable?

B. Calculate the range, variance, and standard deviation for this data series. Which measure

does the best job of describing the dispersion in this variable?

2

Operating experience during the last year suggests the following demand function for its spring water:

Q = 250 - 100P +0.0001Pop + .003I + 0.003A

where Q is quantity in thousands of five-gallon containers, P is price in dollars, Pop is population, I is disposable income per capita,

and A is advertising expenditures.

A. Determine the demand curve faced by CPI in a typical market where P = $ 4, Pop = 4,000,000, I = $ 50,000, and A = $ 400,000.

Show the demand curve with quantity expressed as a function of price, and price expressed as a function of quantity.

B. Calculate the quantity demanded at prices of $ 5, $ 4, and $ 3.

C. Calculate the prices necessary to sell 1,250, 1,500, and 1,750 thousands of five-gallon containers.

3

Operating experience during the past year suggests the following demand function for its knife sets:

Q = 4,000 - 4,000P + 10,000N + .025I + 0.4A

where Q is quantity, P is the price, N is the average rating of television programs during which SEI advertises knives, I

is average disposable income per household, and A is advertising expenditures.

A. Determine the demand curve faced by SEI in a typical market where P = $ 35, N = 18.5

I = $ 44,000, and A = $ 500,000. Show the demand curve with quantity expressed as a function of price, and

price expressed as a function of quantity.

B. Calculate the quantity demanded at prices of $ 40, $ 35, and $ 30.

C. Calculate three prices necessary to sell 264,000, 292,000, and 320,000 sets of knives.

#### Solution Preview

See attached spreadsheet for full explanation.

1

The number of deliveries per week for a sample of six customers.

3 4 5 6 2 4

A. Calculate the mean, median, and mode measures of central tendency for the number of deliveries per week.

Which measure does the best job of describing central tendency for this variable?

mean 4.00

median 4.00

mode 4.00

In this case each measure provides exactly the same answer. Each measure is unique in explaining central tendency and have its own merit. In this case however any measure provides a good measure of central tendency.

B. Calculate the range, variance, and standard deviation for this data series. Which measure

does the best job of describing the dispersion in this variable?

range 4.00

variance 2.00

std.dev. 1.41

Range is a crude measure in general since its just the distance between min and max of the set. variance is useful in that it gives us a measure of spread around the mean. Standard deviation does the same but it is normalized in the sense that if we assume a normal distriubtion we know that roughly 68% of the points will lie within one deviation of the mean, 95% will lie within two ...

#### Solution Summary

The following solution begins with a demonstration of how to find various statistical measures of central tendency and spread. The second part involves solving for values algebraically given various demand equations.