1-1 Discretionary and Essential Expenses-1 Banking 10/20/2017 1-1 Discretionary and Essential Expenses-1 OBJECTIVES Identify the difference between essential and discretionary expenses. Determine the mean, median, and mode of a data set. Use sigma notation to represent and determine the mean of a data set. Chapter 1

1-1 Discretionary and Essential Expenses-2 Banking 10/20/2017 1-1 Discretionary and Essential Expenses-2 OBJECTIVES Create and interpret a frequency distribution table. Determine the mean, median, and mode of a data set presented in a frequency distribution table. Chapter 1

Key Terms mean gross income median disposable income mode essential expense discretionary expense statistics data measures of central tendency mean median mode subscript index outlier skewed data set frequency distribution

What do you need? What do you want? What are the costs associated with items you need to make a living? What are the costs associated with items you want to have but don’t need? How do you budget for each?

$ Money Matters How many times a day do you spend money? The average person spends money 3 times a day Just one soft drink a day for .99cents = $361.35/year The biggest expense item for students? FOOD! Money brings happiness; Money problems bring unhappiness Finances affect everything else in your life! $

Income Income is money earned. Gross income is your income before taxes. Net income is your income after taxes are paid.

Expenses Types of expenses: fixed, variable and discretionary An expense is a cost to meet a need or pay a debt Types of expenses: fixed, variable and discretionary Needs are essential expenses Food Shelter Clothing Transportation Wants are extra expenses Eating out Expensive houses or cars Shopping until you drop The newest technology…..whether it’s an iPhone, iPad, Kindle, etc.

Fixed Expenses A cost that occurs regularly and doesn’t vary in amount. Rent or Mortgage Car payment Insurance School loans Cell phone Cable/Internet Others?

Variable Expenses Costs that occur regularly but may vary in amount. Electricity Water Gas Groceries Others?

Discretionary Expenses A cost determined by personal wants that can be controlled. Movies, videos, music, et cetera Sports Eating out Grooming and clothes Concerts and plays Vacation Credit card Others?

Measures of Central Tendency Mean: Median is the number in the middle when the numbers in a set of data are arranged in ascending or descending order. If the number of numbers in a data set is even, then the median is the mean of the two middle numbers. Mode is the value that occurs most frequently in a set of data. is the most common measure of central tendency. It is simply the sum of the numbers divided by the number of numbers in a set of data. This is also known as average.

Mean (Arithmetic Mean) To calculate the arithmetic mean of a set of data we must first add up (sum) all of the data values (x) and then divide the result by the number of values (n). Since Σ is the symbol used to indicate that values are to be summed (see Sigma Notation) we obtain the following formula for the mean X = 1 𝑛 Σ Xi

: Example Find the mean of 6, 8, 11, 5, 2, 9, 7, 8 X = 1 𝑛 Σ Xi 𝟔+𝟖+𝟏𝟏+𝟓+𝟐+𝟗+𝟕+𝟖 𝟖 = 𝟓𝟔 𝟖 = 7

Example 1 Alena knows that her morning cup of coffee is most definitely a discretionary expense. She pays $2.75 for a 9-oz cup and was wondering if that is a typical price. On Monday, she asked six of her coworkers what they paid for a 9-oz cup of coffee. Their costs per cup were $2.85, $2.15, $1.95, $3.00,$2.05, and $2.40. How can Alena compare her expense with those of her coworkers?

Example 1 CHECK YOUR UNDERSTANDING Nora is a college student. She needs to make an essential textbook purchase for one of her classes. She researches the cost of the book at her college bookstore, some local booksellers, and some online merchants. The prices per book are $128, $118, $96, $102, $100, $118, $118, and $102. Find the mean of the textbook prices.

Example 2 Use the information about coffee prices in Example 1 to represent the formula for the mean price using a compact notation.

Example 2 CHECK YOUR UNDERSTANDING Addy’s monthly water bills for last year are $27, $31, $30, $26, $25, $27, $37, $33, $32, $28, $26, $26. Express the formula for the mean using sigma notation and calculate the mean water bill for the year.

EXTEND YOUR UNDERSTANDING Suppose Addy only wanted the mean of the second through the seventh months. Write the formula for this situation in sigma notation.

Example 3 Anthony wants to make a discretionary purchase of a basic laptop computer. He checks the prices of a particular make and model listed by seven different vendors on a shopping comparison website. He found these prices: $850, $798, $2,400, $790, $836, $700, $780. He computes the mean as $1,022. This number doesn’t seem to be a good representation of the data. How can he find a better representation?

Example 3 CHECK YOUR UNDERSTANDING Construct a set of data for a different discretionary expense containing an odd number of scores with the same median as found in Example 3. Identify the type of expense you chose. Explain how the median is the same as the median in Example 3, although the rest of the data are different.

Example 4 Suppose that in Example 3, Anthony had only found the first six laptop prices when he conducted his online search. Determine the median of those prices.

Example 4 CHECK YOUR UNDERSTANDING Construct a set of data for a different discretionary expense containing an even number of scores with the same median as found in Example 4. Identify the type of expense you chose. Explain how the median is the same as that in Example 4, although the rest of the data are different.

Example 5 A survey was conducted of 880 college students attending the same university. They were offered a list of 10 different Internet service providers and were asked to select the one they prefer. Can a service provider receiving only 89 votes come out on top?

Example 5 CHECK YOUR UNDERSTANDING Construct a data set for a discretionary expense, other than those above, for which the mode is 56.

Example 6 Transportation expenses to and from work are considered essential expenses. Charlie Jane would like to reduce this essential expense by biking to work rather than taking her car. She found 30 different ads both online and in print for the make and model of bicycle she wants to purchase. She made a list of the prices in ascending order. 250, 250, 275, 275, 275, 275, 280, 290, 290, 310, 310, 310, 310, 310, 315, 315, 315, 315, 315, 315, 320, 325, 325, 325, 330, 335, 340, 350, 350, 350 She wants to analyze the prices but is having trouble because there are so many numbers. How can she organize these prices in a helpful format?

Frequency Tables Statistics deals with collecting, organizing, and interpreting data. Data are pieces of information, which are often numerical. Large amounts of data can be organized in a frequency table. A frequency table shows the number of pieces of data that fall within given intervals.

Frequency Tables Words to Know Shows the number of pieces of data that fall within given intervals. Price $ Tally Frequency 1-25 4 26-50 11 51-75 7 76-100 13 Scale- includes the least value and greatest value Interval- Separates the scale into equal parts

Make a frequency table Step 1- Choose an appropriate interval and scale. Should include the least and the greatest value. Step 2- Draw a table with 3 columns and label the columns. Step 3- Complete the table.

Example 6 CHECK YOUR UNDERSTANDING Use the frequency distribution from Example 6 to find the number of bicycles selling for less than $320.

Example 7 Find the mean of the bicycle prices from Example 6.

Example 7 CHECK YOUR UNDERSTANDING What is the mode of the data set for the frequency table in Example 6?