Question

Type of Expense                                                               Cost
Clothing	370.00
Credit card payments	730.00
Mortgage payment	1,920.00
Student loan payments	811.00
Vacation expenses	987.00
Car repair payment	193.00
Groceries	224.00

Use the table above to answer the following questions. Show ALL of your work for full credit.

1. Calculate the mean, median, and mode cost of last month’s expenses.

2. Calculate the range and interquartile range (IQR) of last month’s expenses.

Remember, to find the IQR:

Step 1: Put the numbers in order.

Step 2: Find the median.

Step 3: Place parentheses around the numbers above and below the median.
Step 4: Find Q1 and Q3

Step 5: Subtract Q1 from Q3 to find the interquartile range.

3. Which of the expenses (if any) in the table above is an outlier? Why?

Remember, an outlier is defined as being any point of data that lies over 1.5 IQRs below the first quartile (Q1) or above the third quartile (Q3) in a data set.

High = (Q3) + 1.5 IQR

Low = (Q1) – 1.5 IQR

4. Find the variance and standard deviation. How many standard deviations is the cost of the mortgage payment from the mean cost of all expenses.

5. Explain the difference between the mean and the median. Also, indicate whether the data is skewed or not. Why?

I need help finding number 3 and 4! I believe the range is 1727 and the IQR is 441, but what is the outliers, variance and standard deviation?

Answer 1

Type of Expense	Cost
Clothing	370
Credit card payments	730
Mortgage payment	1,920
Student loan payments	811
Vacation expenses	987
Car repair payment	193
Groceries	224
Total	5235
Mean	747.86

1) Total Expenses =5235

Number of types of Expenses = 7

Therefore, Mean =Total Expenses/Number of types of Expenses

= 5235/7

=747.86

For finding Median, first arrange the data in ascending or descending order as

Cost
193
224
370
730
811
987
1,920

Here number of observation is 7 which is odd.

Median will be in (7+1)/2 term i.e.,4th term

Therefore, Median = 730

To find the mode, or modal value, it is best to put the numbers in order. Then count how many of each number. A number that appears most often is the mode.

Here ,for the given data, there is no number which appear the most.

Therefore there is no Mode for the give data.

2) Range = Maximum value of the observation - Minimum value of the observation

= 1920 - 193

= 1727

Steps for finding Interquartile range

• Step 1: Put the numbers in order.
  193 , 224 , 370 , 730 , 811 , 987 , 1920.
• Step 2: Find the median.
  193 , 224 , 370 , 730 , 811 , 987 , 1920.
• Step 3: Place parentheses around the numbers above and below the median.
  Not necessary statistically, but it makes Q1 and Q3 easier to spot.
  (193 , 224 , 370) , 730 , (811 , 987 , 1920).
• Step 4: Find Q1 and Q3
  Think of Q1 as a median in the lower half of the data and think of Q3 as a median for the upper half of data.
  (193 , 224 , 370) , 730 , ( 811 , 987 , 1920).. Q1 = 224 and Q3 = 987.
• Step 5: Subtract Q1 from Q3 to find the interquartile range.
  987 - 224 = 763

Therefore Interquartile range =763

3) Here, Q1=224

Q3= 987

IQR=763

So, high = Q3 +1.5 IQR =987 + (1.5*763) = 2131.5

low= Q1 - 1.5 IQR =224 -(1.5*763) = -920.5

An outlier is defined as being any point of data that lies over 1.5 IQRs below the first quartile (Q1) or above the third quartile (Q3) in a data set.

We have to check whether the data is outside the Range (-920.5 , 2131.5)

There is no data which is outside the given range. So, there is no Outlier in the given data.

4)

Type of Expense	Cost	X- mean	(x-mean)^2
Clothing	370	-377.86	142778.18
Credit card payments	730	-17.86	318.98
Mortgage payment	1,920	1172.14	1373912.18
Student loan payments	811	63.14	3986.66
Vacation expenses	987	239.14	57187.94
Car repair payment	193	-554.86	307869.62
Groceries	224	-523.86	274429.30
Total	5235		2160482.86
Mean	747.86

Variance =

=

= 308640.41

Standard Deviation =

Variance of the cost of the mortgage payment from the mean cost of all expenses =

   =

   =196273.17

Therefore Standard Deviation of the cost of the mortgage payment from the mean cost of all expenses

=