HOMEWORK 1 Data Analysis for Hospitality Managers(Due: Apr. 15th)

Rahel Hailu

1. Last year an accounting firm paid each of its six clerks $25,000, its two junior

accountants $60,000 each, and the firm’s owner $255,000.

a. What is the mean salary paid at this firm? How many of the employees earn less

than the mean? What is the mode and median of salary?

Mean= (25,000*6+60,000*2+225,000)/9 = $55,000

Mode=$25,000

Median=$25,000

b. Find the range and IQR. Which one is a better measure of dispersion? Why?

Range= 225,000-25,000=200,000

Q1= 0.25*9 = 2.25cases------ 25,000

Q3= 0.75*9= 6.75 cases------ 60,000

IQR= 35,000 (60000-25000), this one is better than range, in case of range there

are outliners, it shows range bigger, however IQR is better measurement than

range.

c. This year, the same firm gives no raise to the clerks and junior accountants, while

the owner’s take increases to $455,000. How does this change affect the mean?

How does it affect the median? (You don’t have to recalculate the mean and

median!! Just guess.)

Since the owner salary increases from 255,000 to 455000, definitely it affects

mean, though the median still the same.

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(SPSS)

Using the data file “marketing” to answer following questions.

1. There are 8 variables except for ID. Fill the box below.Variables Level of

MeasurementAppropriate Central Tendency Measure

Appropriate Dispersion Measure

Visday Nominal Mode None

Vistime Nominal Mode None

Menu Nominal Mode None

recommend Ordinal Median IQR

Satisfied Ordinal Median IQR

Amount Scale Median/ mean SD

Income Ordinal Mode/ Median SD

frequency Scale Mode/Median SD

2. Produce a frequency table and a bar chart for “menu”.

menu category

Frequency Percent Valid Percent

Cumulative

Percent

Valid healthy food 141 31.3 31.3 31.3

seasonal food 210 46.7 46.7 78.0

regular food 99 22.0 22.0 100.0

Total 450 100.0 100.0

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3. Produce a proper kind of graph to show the distribution of “amount.”

4. Based on the graph you made in question 3, describe the shape of the distribution. Guess which one would be higher, mean or median? Why?

Positive skewness - long tail in the right side.Long tail in the right side, - Mean is higher than median;

5. Confirm your answer to the question 4 by finding appropriate measures of central tendency.

Refer to question #1, “Amount” is scale. Therefore, Central tendency are mean and median

6. Find the range, IQR, and standard deviation of the variable “amount”.

The Range is 74,300 The IQR is 75%-25%-- 14,900 (36,900-22,000).And the SD is 11120.853

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Statistics

amount spent

N Valid 450

Missing 0

Mean 29940.00

Median 29750.00

Range 74300

Percentiles 25 22000.00

50 29750.00

75 36900.00

7. Find the median, range, and IQR of “amount” for each of daytime visitors and evening visitors, separately.

Statistics vistime = 1

amount spent

NValid 180

Missing 0

Median 25100.00

Range 40500

Percentiles

25 20300.00

50 25100.00

75 30825.00

Statistics vistime = 2

amount spent

NValid 270

Missing 0

Median 32650.00

Range 73200

Percentiles

25 26200.00

50 32650.00

75 37900.00

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8. Make a box-plot for amount for all visitors, and also for daytime visitors and evening visitors, separately. Describe what you find in a couple of sentences.

In comparison to the amount for daytime and night time visitors, evening visitors amount

are higher than daytime visitors. Therefore, amount for evening consumers are superior

than daytime.

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9. Get the means and standard deviations for each of daytime visitors and evening visitors. Which group spent more? Which group is diverse in the amount spent?

Statistics- Daytime

amount spent

NValid 180

Missing 0

Mean 25490.00

Std. Deviation 8556.771

Statistics- Evening

amount spent

NValid 270

Missing 0

Mean 32906.67

Std. Deviation 11645.716

Mean and the SD - evening visitors paying are higher than daytime visitors.-Evening visitors spent more than daytime.- Std. Deviation shows, distribution diverse of the amount. Henceforth, the evening visitors groups have diversification than the daytimevisitors.

10. Final question. Do you think that the difference between the two groups (daytime vs. evening) in the mean amount is large enough to conclude that one group spent more than the other? Why or why not? (This topic will be covered in the inferential statistics later. For now, just guess and tell your ‘impression.’)

I could not determine the mean of day and evening groups spent than one each other’s, because there are still insignificant error in the sample.

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