Business Statistics
DESCRIPTIVE STATISTICS
DESCRIPTIVE STATISTICS
6. In a sample of 50 businesses in Liechtenstein, ten had between 10 and 19 employees; fourteen had between 20 and 29 employees; seventeen had between 30 and 39 employees; seven had between 40 and 49 employees; and two had between 50 and 59 employees.
a. Construct a Frequency Table for this data. Include columns for Frequency, Relative Frequency, Cumulative Frequency, and Cumulative Relative Frequency.
6. In a sample of 50 businesses in Liechtenstein, ten had between 10 and 19 employees; fourteen had between 20 and 29 employees; seventeen had between 30 and 39 employees; seven had between 40 and 49 employees; and two had between 50 and 59 employees.
b. Draw a bar chart for this data.
7. The following data are the number of automobiles sold last month by fifteen car dealers in Austria.
116 120 122 130 136 137 142 142 147 160 162 168 170 172 173
Construct a Stem-and-Leaf display for this data.
8. The following scatterplot contains twenty observations for two generic variables, “x” and “y”.
Based on this scatterplot, would you classify the relationship between x any y as being Positive, or Negative, or Null? Why?
There is a Negative relationship between “x” and “y”. Clearly “y” tends to decrease as “x” increases (that is, the two variables tend to move in opposite directions). Note: In this scatterplot I changed the value at which the horizontal axis and the vertical axis cross (i.e., the graph’s origin; it is not the “usual” x=0 and y=0), the minimum and maximum values of each axis, and the size of the gaps between tic marks on each axis. Sometimes you see that in real-world applications ... which is why I did it here!
9. The Excel data file “Tax Cost” (which is with the rest of this week’s stuff on Moodle) contains the cost paid by families to have their income taxes prepared in the USA. (Trust me, tax forms there can get very complicated....). Use Excel to calculate, and then explain and interpret, the following statistics:
a. Mean
a. Using the AVERAGE command in Excel (as per the lecture), we find the mean to be 160. On average, a family in our sample paid $160.00 to have their income taxes prepared.
9. The Excel data file “Tax Cost” (which is with the rest of this week’s stuff on Moodle) contains the cost paid by families to have their income taxes prepared in the USA. (Trust me, tax forms there can get very complicated....). Use Excel to calculate, and then explain and interpret, the following statistics:
b. Median
b. Using the MEDIAN command in Excel (as per the lecture), we find the median to be 135. One-half of the families paid less than $135, and the other half paid more than $135, to have their taxes prepared.
9. The Excel data file “Tax Cost” (which is with the rest of this week’s stuff on Moodle) contains the cost paid by families to have their income taxes prepared in the USA. (Trust me, tax forms there can get very complicated....). Use Excel to calculate, and then explain and interpret, the following statistics:
c. Mode
c. Using the MODE command in Excel (as per the lecture), we find the mode to be 120. The most common amount a family in our sample paid to have their taxes prepared is $120.
9. The Excel data file “Tax Cost” (which is with the rest of this week’s stuff on Moodle) contains the cost paid by families to have their income taxes prepared in the USA. (Trust me, tax forms there can get very complicated....). Use Excel to calculate, and then explain and interpret, the following statistics:
d. First Quartile
d. Using the QUARTILE command in Excel (as per the lecture), we find the first quartile (Q1) value to be 115. One-quarter (25%) of the families in our sample paid $115 or less to have their taxes prepared.
9. The Excel data file “Tax Cost” (which is with the rest of this week’s stuff on Moodle) contains the cost paid by families to have their income taxes prepared in the USA. (Trust me, tax forms there can get very complicated....). Use Excel to calculate, and then explain and interpret, the following statistics:
e. Third Quartile
e. Using the QUARTILE command in Excel (as per the lecture), we find the third quartile (Q3) value to be 183.75. Three-quarters (75%) of the families in our sample paid $183.75 or less to have their taxes prepared.
9. The Excel data file “Tax Cost” (which is with the rest of this week’s stuff on Moodle) contains the cost paid by families to have their income taxes prepared in the USA. (Trust me, tax forms there can get very complicated....). Use Excel to calculate, and then explain and interpret, the following statistics:
f. 90 Percentile
f. Using the PERCENTILE command in Excel (as per the lecture), we find the 90th Percentile (P90) value to be 237. 90% of the families in our sample paid $237 or less to have their taxes prepared.
9. The Excel data file “Tax Cost” (which is with the rest of this week’s stuff on Moodle) contains the cost paid by families to have their income taxes prepared in the USA. (Trust me, tax forms there can get very complicated....). Use Excel to calculate, and then explain and interpret, the following statistics:
g. Five-Number Summary
g. Using the MIN and MAX commands in Excel, we find the lowest value is 100 and the highest value is 360. So the Five Number Summary is: 100, 115, 135, 183.75, 360
10. The following data measure the price of a stock at the end of six consecutive quarters. 182 168 184 190 170 174 Use your calculator (not Excel) to calculate the following statistic values.
a. Mean
b. Variance
c. Standard Deviation
11. The cost of renting a car for one month in Switzerland varies depending on location and the type of car being rented. Suppose this cost has a mean of 3,100 CHF and a standard deviation of 1,200 CHF. Calculate the standardized value for each of the following costs. Then interpret each of these Z-score values. Finally, explain why each value either would or would not be considered an outlier here.
a. 2,300 CHF
b. 4,900 CHF
c. 13,000 CHF
12.
b. Examining the graph in part “a” we see that there appears to be a positive linear relationship. (The variables tend to move in the same direction; e.g., as one goes up, the other also tends to go up.)
c. Using the CORREL command in Excel (as per the lecture), we find the correlation value to be 0.69.
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Flashcards
6. In a sample of 50 businesses in Liechtenstein, ten had between 10 and 19 employees; fourteen had between 20 and 29 employees; seventeen had between 30 and 39 employees; seven had between 40 and 49 employees; and two had between 50 and 59 employees.
a. Construct a Frequency Table for this data. Include columns for Frequency, Relative Frequency, Cumulative Frequency, and Cumulative Relative Frequency.
6. In a sample of 50 businesses in Liechtenstein, ten had between 10 and 19 employees; fourteen had between 20 and 29 employees; seventeen had between 30 and 39 employees; seven had between 40 and 49 employees; and two had between 50 and 59 employees.
b. Draw a bar chart for this data.
7. The following data are the number of automobiles sold last month by fifteen car dealers in Austria.
116 120 122 130 136 137 142 142 147 160 162 168 170 172 173
Construct a Stem-and-Leaf display for this data.
8. The following scatterplot contains twenty observations for two generic variables, “x” and “y”.
Based on this scatterplot, would you classify the relationship between x any y as being Positive, or Negative, or Null? Why?
There is a Negative relationship between “x” and “y”. Clearly “y” tends to decrease as “x” increases (that is, the two variables tend to move in opposite directions). Note: In this scatterplot I changed the value at which the horizontal axis and the vertical axis cross (i.e., the graph’s origin; it is not the “usual” x=0 and y=0), the minimum and maximum values of each axis, and the size of the gaps between tic marks on each axis. Sometimes you see that in real-world applications ... which is why I did it here!
9. The Excel data file “Tax Cost” (which is with the rest of this week’s stuff on Moodle) contains the cost paid by families to have their income taxes prepared in the USA. (Trust me, tax forms there can get very complicated....). Use Excel to calculate, and then explain and interpret, the following statistics:
a. Mean
a. Using the AVERAGE command in Excel (as per the lecture), we find the mean to be 160. On average, a family in our sample paid $160.00 to have their income taxes prepared.
9. The Excel data file “Tax Cost” (which is with the rest of this week’s stuff on Moodle) contains the cost paid by families to have their income taxes prepared in the USA. (Trust me, tax forms there can get very complicated....). Use Excel to calculate, and then explain and interpret, the following statistics:
b. Median
b. Using the MEDIAN command in Excel (as per the lecture), we find the median to be 135. One-half of the families paid less than $135, and the other half paid more than $135, to have their taxes prepared.
9. The Excel data file “Tax Cost” (which is with the rest of this week’s stuff on Moodle) contains the cost paid by families to have their income taxes prepared in the USA. (Trust me, tax forms there can get very complicated....). Use Excel to calculate, and then explain and interpret, the following statistics:
c. Mode
c. Using the MODE command in Excel (as per the lecture), we find the mode to be 120. The most common amount a family in our sample paid to have their taxes prepared is $120.
9. The Excel data file “Tax Cost” (which is with the rest of this week’s stuff on Moodle) contains the cost paid by families to have their income taxes prepared in the USA. (Trust me, tax forms there can get very complicated....). Use Excel to calculate, and then explain and interpret, the following statistics:
d. First Quartile
d. Using the QUARTILE command in Excel (as per the lecture), we find the first quartile (Q1) value to be 115. One-quarter (25%) of the families in our sample paid $115 or less to have their taxes prepared.
9. The Excel data file “Tax Cost” (which is with the rest of this week’s stuff on Moodle) contains the cost paid by families to have their income taxes prepared in the USA. (Trust me, tax forms there can get very complicated....). Use Excel to calculate, and then explain and interpret, the following statistics:
e. Third Quartile
e. Using the QUARTILE command in Excel (as per the lecture), we find the third quartile (Q3) value to be 183.75. Three-quarters (75%) of the families in our sample paid $183.75 or less to have their taxes prepared.
9. The Excel data file “Tax Cost” (which is with the rest of this week’s stuff on Moodle) contains the cost paid by families to have their income taxes prepared in the USA. (Trust me, tax forms there can get very complicated....). Use Excel to calculate, and then explain and interpret, the following statistics:
f. 90 Percentile
f. Using the PERCENTILE command in Excel (as per the lecture), we find the 90th Percentile (P90) value to be 237. 90% of the families in our sample paid $237 or less to have their taxes prepared.
9. The Excel data file “Tax Cost” (which is with the rest of this week’s stuff on Moodle) contains the cost paid by families to have their income taxes prepared in the USA. (Trust me, tax forms there can get very complicated....). Use Excel to calculate, and then explain and interpret, the following statistics:
g. Five-Number Summary
g. Using the MIN and MAX commands in Excel, we find the lowest value is 100 and the highest value is 360. So the Five Number Summary is: 100, 115, 135, 183.75, 360
10. The following data measure the price of a stock at the end of six consecutive quarters. 182 168 184 190 170 174 Use your calculator (not Excel) to calculate the following statistic values.
a. Mean
b. Variance
c. Standard Deviation
11. The cost of renting a car for one month in Switzerland varies depending on location and the type of car being rented. Suppose this cost has a mean of 3,100 CHF and a standard deviation of 1,200 CHF. Calculate the standardized value for each of the following costs. Then interpret each of these Z-score values. Finally, explain why each value either would or would not be considered an outlier here.
a. 2,300 CHF
b. 4,900 CHF
c. 13,000 CHF
12.
b. Examining the graph in part “a” we see that there appears to be a positive linear relationship. (The variables tend to move in the same direction; e.g., as one goes up, the other also tends to go up.)
c. Using the CORREL command in Excel (as per the lecture), we find the correlation value to be 0.69.
