Data Set: Apartment Rents (in ascending order)

# Household Debt 1 122.231 18.927 2 125.409 52.055 3 59.025 53.880 4 116.128 57.380 5 60.370 58.458 6 69.402 7 142.762 59.423 8 131.934 9 107.320 68.140 10 11 72.140 12 72.576 13 148.782 79.649 14 94.513 15 97.544 16 131.176 17 110.354 18 19 20 124.831 21 22 23 24 25 Total 2.234.409

In the year 2000, the average salaries of elementary school teachers in Oregon, Washington and Alaska were (in thousands USD) 40.9, 41.1 and 47.3. Given that there were 19.7, 28.1 and 5.3 thousand teachers in these states. Find the average salary of all the elementary school teachers in the three states.

A wholesaler sold 575, 410 and 520 microwave ovens at prices (in USD) 75, 125 and 100 respectively. What is the mean price of the ovens sold?

The number of employees of the municipalities in a certain area of a country were given in the following table Find the mean and modal class? # Frequency 202-204 2 205-207 7 208-210 16 211-213 26 214-216 18 217-219 4

THE MODE - If a data set has only one value that occurs with greatest frequency is said to be UNIMODAL If a data set has two values that occur with the same greatest frequency is said to be BIMODAL If a data set has more than two values that occur with the same greatest frequency, each value is used as the mode, and the data set is said to be MULTIMODAL When no data value occurs more than once, the data set is said to have NO MODE

Example: The following data represent the duration (in days) of Space Shuttle voyages for the years 1992-1994. (18 values) 8,9,9,14,8,8,10,7,6,9,7,8,10,14,11,8,14,11 Q: Find The Mode

Example: A manager of clothing store wants to approximate the median age of both his male and female customers so that he can take this into account when ordering stock. The following data are obtained (age in years) Female (x) Male (y) 15 60 17 20 24 35 27 30 42 12 17 29 37 40 72 Q: Find the median age in years for both female and male customers

Example: These data are obtained on the sales per day in thousand of TRL at two franchises of the same hamburger chain. Franchise A Franchise B 0,9 2,5 1,4 2,6 1,7 3,2 3,6 1,3 2,9 3,8 2,7 5,9 3,5 0,7 4,8 4,7 0,9 0,7 4,5 0,6 4,6 0,3 5,3 1,4 3,1 5,2 4,2 2,5 5,1 1,7 5,0 A- Find the sample mean for each franchise. Based on statistics, does it appear that the average sales per day for A is about the same as that for B? Explain. B- Find the sample median for each franchise. Based on statistics, does it appear that the average sales per day for A is about the same as that for B? Explain. C- Is it safe to say the distribution of sales per day is the same for these two franchises? Be Careful!!!! Look at the stem-and-leaf displays for the two data sets.

MONTHLY STARTING SALARY (In TRL) Graduate Monthly Starting Salary 1 2,850 2 2,950 3 3,050 4 2,880 5 2,755 6 2,710 7 2,890 8 3,130 9 2,940 10 3,325 11 2,920 12 TOTAL: 35,280

Properties of the Mean 1- The Mean can be calculated for any set of NUMERICAL Data 2- The Mean is unique and unambiguous value. 3- The means of several sets of data can always be combined into the overall mean of all the data. 4- If each value in a sample were replaced by the mean, then ∑X would remain unchanged 5- The mean takes into account the value of each item in a set of data. 6- The mean is relatively reliable in the sense that means of many samples drawn from the same population generally do not fluctuate, or vary, as widely as other statistics used to estimate the mean of a population.

Properties of the Median In addition to the properties of the Mean; 1- It splits the data into two parts 2- The median is preferable to the mean because it is not so easily affected by extreme values.

Second Class= 40 students Third Class= 25 students Problem: Imagine that four classes in Math 119 course obtained the following mean scores on the final examination; 75, 78, 72 and 80. Q: Could you sum these four means together and divide by 4 to obtain an overall mean for all of the four classes? A: This could be done only if the n (the number of students) in each class is identical What if; First Class = 30 students Second Class= 40 students Third Class= 25 students Fourth Class= 50 students Then the weighted mean is =?

Problem: The following list gives the duration in minutes of 24 power failures. 18 125 44 96 31 53 26 80 49 125 63 58 45 33 89 12 103 127 75 40 80 61 28 129 Find the median.