Hotel accommodation

Task 2

Write a statistical question or hypothesis, which involves comparing the two sets of

data.

• Your question or hypothesis or must:• be clear and not open to more than one interpretation• allow you to calculate statistics and draw graphs to

investigate the relationship between the variables.

• allow you to respond to your question or hypothesis and justify your answer with reference to features of your data, statistics, and graphs.

Questions

• On average, is it more expensive to stay in a hotel in Auckland or a hotel in Wellington?

• Which city has the most expensive hotel?

• Which city has the biggest range of prices?

Questions

• On average, is it more expensive to stay in a hotel in Auckland or a hotel in Wellington?

• Which city has the most expensive hotel?

• Which city has the biggest range of prices?

• These are all comparison questions.

Use the data for Auckland Hotels and Wellington Hotels to respond to your

question or hypothesis.

• The following instructions will help you to do this.• 1. Calculate statistics for each of the variables Auckland

Hotel prices and Wellington Hotel prices. These must include at least one measure of central tendency and at least one measure of spread

• 2. Draw appropriate graph(s) that allow you to compare the data sets.

• 3. Respond to your question or hypothesis. • Explain your answer by referring to your statistics and

graphs. • You should make at least 2 statements that support

your response.

Calculate statistics for each of the variables Auckland Hotel prices and Wellington Hotel prices. These must

include at least one measure of central tendency and at least one measure of spread.

• A central tendency means a mean, median or mode.

• A mean is the average of the prices.

• A median is the middle value.

• A mode is the most common value

To calculate the mean.

• We could add them all up and divide by how many there are.

• This would take some time and we could make a mistake.

• A good way of making sure it is accurate is to use an Excel spreadsheet.

• We use the formula =average(data)

To calculate the median.

• We need to find the middle value• This would take some time and we

could make a mistake.• A good way of making sure it is

accurate is to use an Excel spreadsheet.

• We use the formula =median(data)

To calculate the mode.

• We need to find the most common value

• A good way of making sure it is accurate is to use an Excel spreadsheet.

• We use the formula =mode(data)• Sometimes Excel only finds one value

when there are two.

These are the results

Auckland has a higher mean

Wellington has a higher median

Wellington has a higher mode

Is this an important statistics in this investigation?

We need to know more.

Measures of spread.

• We can find the range of values. This means the largest to the smallest.

• Auckland has a range of 399 - 75 = 324

• Wellington has a range of 210 - 85 = 125.

• Auckland prices are more spread out.

Measures of spread.

• Another measure of spread is the interquartile range - This means the difference between the upper and lower quartiles (quarters).

• First we need to find the quartiles.• Excel can do this for us.• We use the equation =quartile(data,1) for the

lower quartile and• =quartile(data,3) for the upper quartile.• We could find them ourselves by counting the

data.

Our statistics look like this now.

The interquartile range tells us there is about the same spread in the middle section of the data

Draw appropriate graph(s) that allow you to compare the data sets.

• We need a graph that shows us all this information.

• A dot plot or box and whisker graph are the best for comparisons.

DOT PLOT IN FATHOM

BOX PLOT IN FATHOM

It’s more complicated if we use EXCEL

First we set up a chart for Auckland

Then we set up a chart for Wellington

Use these formulas

Draw the graph

Conclusions

• What are your conclusions?

• An outlier in the data for Auckland shows an outlier but otherwise, we would conclude that the prices do not vary much.

Conclusions

The interquartile ranges are approximately the same.

The range is much greater for Auckland due to an outlier and hence the interquartile range is a better measure of the spread.

Conclusions

• Refer to your Central tendencies:

• The means are approximately the same.

• The median price in Wellington is higher.

• The mode is irrelevant.

Conclusions

• As the boxes overlap we could not conclude that there is a significant difference between hotel prices in Wellington and Auckland.

Evaluation

• To evaluate the process, go back and read the original information that was provided.

Evaluation

• Mary used the AA Accommodation guide 2001 for the North Island to collect her data.

• This is only one source of information and it does not allow for all hotels to have a chance of being selected as not all hotels are listed.

• That data comes from 2001 which is now likely to be outdated as prices may have changed.

Evaluation

• For Auckland Hotels she selected the first 32 listed hotels that gave prices.

• The first 32 listed hotels may not represent the situation appropriately as their prices may be different from hotels later in the listings.

Evaluation

• For Wellington Hotels she was only able to obtain 27 prices. 

• This was the total amount available. The fact that there are fewer values than those given for Auckland does not matter.

Evaluation

• The prices quoted are for a couple for one night.

• Prices may vary according to how many use the room and hence may not reflect the situation for families or single occupation.

• It means that our analysis is only valid for this situation.

Evaluation

• Where a range of prices was given she took the median and, if necessary, rounded it to the nearest dollar.

• Again this limits the relevance of the outcomes as we may not be comparing ‘apples for apples’.