Finite Math Take-home Test (randolph)

Batool Alsamadi Finite Math - Randolph MWF 11:00 - 11:50 am Apr 13, 2007 due

I. Discuss the three ways of visually representing data? Describe them, tell when and how they’re used? 1) Bar Graph -Equally spaced, and each bar has the same width as the rest. -This method is usually used for comparisons. 2) Pie Graph -A circle that is divided into “slices of a pie” where each slice corresponds to a category of the data. The area of each slice is proportional to the percentage of items in that category. This is done by making the center angle of each slice equal to 360 degrees times the percentage associated with the segment. -This method is used to present data in percentiles or figures given in fractions. 3) Histogram -Just like a bar graph; except no spaces. -Can be automatically converted into a line graph by placing a dot in the center of each bar, and then connecting the dots. -Each bar is centered over its corresponding data. This is done by having the bottom of each bar extend a ½ hunt on each side of it’s data. For example, if a bar is representing the data of “12” then the base of the bar extends from 11 ½ to 12 ½. -This method is used for looking for trends. It’s usually used in data that consists a collectin of numbers. For example, the data could consist of ages, weights, test scores, etc.

II. How are medians and quartiles calculated for data? Medians / Calculation: -The median is the center-most data in a set. The median data is the data that divides the bottom 50% of the rest of the data from the top 50%. The median is also known as the 2nd Quartile. -To find the median in a set, the data must be first arranged in increasing or decreasing numerical order. -The median is the “middle” data if the set has an odd amount of data -If the set has an even amount of data, the median then is the average of the two “middle” data’s. e.g. Let’s say the data we’re given is x: 0 1 2 3 4 5 6 7 8 y: 7 6 4 5 2 1 3 0 8 ….we place the data in order so that: { 0 1 2 3 4 5 6 7 8} *The median in this set is 4. However, in the case of an even amount of data in a set, we would end up with two center-most data’s as the median, so in this case we would find the mean of these two data’s: e.g. {1 2 3 4 5 6 7 8} *Since the medians are both 4 and 5, we find the mean of 4 and 5, so the median of this set is: 4 + 5 = 9 / 2 = 4 ½ The median is 4 ½. Quartiles/ Calculation: -The data must be first arranged in numerical order to compute the quartiles. -Each quartile divides the data into approx. 4 equal parts, each part roughly

consisting of 25%. -Each quartile is used for information about the dispersion of the data. -The Interquartile Range is the middle 50% of where the data lies, or Q3-Q1 (the data that lies in the regions of the first quartile to the third quartile):

-Another way to think about it, Q1 is 25%; Q2 is 50%; Q3 is 75%; and Q4 is 100%. e.g. If the data set below is given: {1

2 3 4 5 6 7

8} *Then, Q1=2; Q2=4; Q3=6; Q4=8.

e.g. If the data set given has a median that arrives at two numbers {the average of the middle two numbers}, the quartiles would be computed this way: {1 4 7 11 16 22 29 37 46 56} *The min=1; the max=56; the next number we should find is the median: 16 + 22 = 38 / 2 = 19. Thus, Q2 (median) = 19. -The to the left of the median are 1, 4, 7, 11, and 16, and the numbers to the right of the median are 22, 29, 37, 46, and 56. -Therefore, Q1=7; Q2=19; Q3=37; Q4=56. -For the interquartile range, these lists have medians 7 and 37, respectively. Therefore, the interquartile range is Q3 - Q1 = 37 - 7 = 30.

III. What is a frequency distribution? A relative frequency distribution? A probability distribution? How are they different? How are they similar? How are they used? Frequency Distribution -Data collected from surveying and presented in a form where for each possible value of a statistical variable there’ll be a tabulated number of occurrences. -A frequency distribution lists out all the outcomes “x” of the experiment and the number “y” of times each occurred. -A frequency distribution is the most efficient form to analyze data that comes from survey data. -A frequency distribution is different than a relative frequency distribution and a probability distribution because it is used to display and summarize the survey data. Example:

“Table A”

sold Monthly sales 2 3 4 5 6

Cookies sold at Schnuck’ s 3 3 14 21 11

Cookies

at Dierberg’ s 21 0 0 11 13

7 8

5 2

51 13

Relative Frequency Distribution -The relative frequency distribution is different than the frequency distribution and probability distribution because it is used for making comparisons. -The relative frequency distribution is just like frequency distribution, except it uses proportions instead of the actual number of occurrences. -The relative frequency distribution pairs each outcome “x” with its “y” relative frequency. It is calculated for each outcome X1 = Y1/n (“n” is the total number of occurrences); then the relative frequency of outcome X2 is = Y2/n, etc. -The frequency and the relative frequency distributions are both taken directly from the performance of a survey/experiment and the collection of data observed at each trial “x” of the survey/experiment. -The sum of the relative frequency distribution should always add up to 1. “Table B”

Proportion of

Sold Monthly sales 2 3 4 5 6 7 8

Proportion of Cookies Sold

at Schnuck’ s 3/59 3/59 14/59 21/59 11/59 5/59 2/59

.05 .05 .24 .36 .19 .08 .03

Total:

=1

Cookies

at Dierberg’ s

21/109 0/109 13/109

Total:

.19 0 0/109 11/109 .12 51/109 13/109

0 .10 .47 .12

=1

Probability Distribution -Frequency and relative frequency distributions are obtained from actual experiments; whereas the probably distribution are obtained from “theoretical” experiments (interpreted based off data from actual experiments)