1 1 Discretionary and Essential Expenses1 OBJECTIVES Identify

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. Slide 1

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. Slide 2

Key Terms • • gross income disposable income essential expense discretionary expense • statistics • data • measures of central tendency • • mean median mode subscript index outlier skewed data set frequency distribution Slide 3

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. 99 cents = $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 § 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 i. Phone, i. Pad, Kindle, etc.

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

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

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

Measures of Central Tendency Mean: 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. 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.

Mean (Arithmetic Mean)

: Example Find the mean of 6, 8, 11, 5, 2, 9, 7, 8

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, and $102. Find the mean of the textbook prices. Slide 15

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? Slide 19

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, 275, 280, 290, 310, 315, 315, 320, 325, 330, 335, 340, 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? Slide 25

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. Scale- includes the least value and greatest value Interval- Separates the scale into equal parts Price $ Tally Frequency 1 -25 4 26 -50 11 51 -75 7 76 -100 13

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. Slide 30

Example 7 Find the mean of the bicycle prices from Example 6. Slide 31

Example 7 CHECK YOUR UNDERSTANDING What is the mode of the data set for the frequency table in Example 6? Slide 32