Math-110: Understanding Data Analysis Concepts

Define each of the following: a) Element. a) The element of a data set is simply the individual and unique entry in a data set about which data has been collected, analyzed and presented in the same manner. b) Variable. b) A variable is a particular, measurable attribute that the researcher believes is needed to describe the element in their study. 2024 MATH-110 COMBINATION OF EXAMS QUESTIONS WITH 100% SOLVED ANSWERS Define each of the following: a) Element. An element is described as "the individual and unique entry in a data set about which data has been collected, analyzed and presented in a same manner to differentiate" (Module 1). b) Variable. A variable is defined as a "particular measurable attribute that the researcher believes is needed to describe the element in their study" (Module 1). c) Data. Data (or the plural of datumn) is defined as things (such as numerical information, people, geographical areas,etc.) about which information can be collected and then analyzed. Answer Key

Explain the difference between population and sample. Population is the entire number of items in a large group. A sample is representative group from the population. Look at the following data and see if you can identify any outliers: 65 71 55 69 3 77 67 70 246 61 277 Explain the difference between population and sample. "The entire number of items in a large group" would be defined as the population. (Module 1) The sample is then taken from the population by a researcher and is studied.The sample taken from the population is, in fact, the subset of the population. You need the population to get the sample and without the population, there can be no sample. Instructor Comments Very good definitions. Answer Key Look at the following data and see if you can identify any outliers: 65 71 55 69 3 77 67 70 246 61 277 3, 246, 277 Instructor Comments Very good. Answer Key The outliers are: 3 246 277 The following pie chart shows the percentages of total items sold in a month in a certain fast food restaurant. A total of 4900 fast food items were sold during the month. How many were burgers? How many were french fries?

The following pie chart shows the percentages of total items sold in a month in a certain fast food restaurant. A total of 4900 fast food items were sold during the month. How many were burgers? How many were french fries? Burgers : 4900(.32) = 1568 French Fries : 4900(.18) = 882 4900(.32)=1568 32% or 1,568 burgers were sold during the month. 4900(.18)=882 18% or 882 french fries were sold during the month. Instructor Comments Very good. Answer Key During an hour at a fast food restaurant, the following types of sandwiches are ordered: Turkey Hamburger Cheeseburger Fish Hamburger Turkey Fish Chicken Fish Chicken Turkey Fish Hamburger Fish Cheeseburger FishCheeseburger Hamburger Fish Fish Cheeseburger Hamburger Fish Turkey Turkey Chicken Fish Chicken Cheeseburger Fish Turkey Fish Fish Hamburger Fish Fish Turkey Chicken Hamburger Fish Cheeseburger Chicken Chicken Turkey Fish Chicken Hamburger Chicken Fish Chicken a) Make a frequency distribution for this data. Types of Frequency Sandwiches Turkey 8

Chicken 10 Cheeseburger 6 Fish 18 Hamburger 8 Total 50 b) Make a relative frequency distribution for this data. Include relative percentages on this table. Types of Frequency Relative Relative Sandwiches Frequency Percentage Turkey 8 (8/50)= .16 (.16)100 = 16% Chicken 10 (10/50)= .2 0 (.20)100 = 20% Cheeseburg er 12% Fish 6 18 (6/50)= (18/50) = .12 .36 (.12)100= (.36)100 = 36% Hamburger 8 (8/50)= .1 6 (.16)100 = 16% Total 50 1 100% Consider the following data: 422 389 414 401 466 421 399 387 450 407 392 410 440 417 490 Find the 20th percentile of this data. 387,389,392,399,401,407,410,414,417,421,422,440,450,466,490 i=( p n = (20) *15= 3 100 ) 100 i=3 392 is the 20th percentile of this data. Consider the following data: {29, 20, 24, 18, 32, 21} a) Find the sample mean of this data. x* = ∑x i

n x*=(29+20+24+18+32+21) =144 = 24 6 6 b) Find the range of this data. {18,20,21,24,29,32} Range is 14 (32-18)=14 c) Find the sample standard deviation of this data. s 2 =∑(x i -x) 2 = (18-24) 2 + (20-24) 2 +(21-24) 2 +(24-24) 2 +(29-24) 2+ (32-24) 2 = 36+16+9+0+25+64 = 150 =30 n-1 6-1 5 5 s=√s 2 = √30 = 5.477 d) Find the coefficient of variation. cov=standard deviation *100=5.477 *100 =22.82 mean 24 Suppose that you have a set of data that has a mean of 65 and a standard deviation of 10. a) Is the point 75 above, below, or the same as the mean. How many standard deviations is 75 from the mean. x*65 z=x-u = 75-65 =1 o 10 z=1 The point 75 is above the mean (because it is a positive number), meaning that the data point is one standard deviation above the mean.

b) Is the point 85 above, below, or the same as the mean. How many standard deviations is 85 from the mean. x*65 z=x-u = 85-65 =2 o 10 z=2 The point 85 is above the mean (because it is a positive number), meaning that the data point is two standard deviations above the mean. c) Is the point 57.5 above, below, or the same as the mean. How many standard deviations is 57.5 from the mean. x*65 z=x-u = 57.5-65 =-0.75 o 10 z=-0.75 The point 57.5 is below the mean (because it is a negative number), meaning that the data point is .75 standard deviations below the mean. d) Is the point 107 above, below, or the same as the mean. How many standard deviations is 107 from the mean. x*65 z=x-u = 107-65 =4.2 o 10 z=4.2 The point 107 is above the mean (because it is a positive number), meaning that the data point is 4.2 standard deviations above the mean. Consider the following set of data: {22, 14, 35, 49, 8, 18, 30, 44} a) Find the median. {8,14,18,22,30,35,44,49} Median=22+30 =26 26 b) Find the mode of this set. {8,14,18,22,30,35,44,49} No mode (no number appears more than once). Suppose A and B are two events with probabilities: P(A)=.35,P(B c )=.45,P(A∩B)=.25.

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