# Collecting and Analyzing Data

## M7-8 Collecting and Analyzing Data

*Show all work to receive credit. Write verbal questions in at least one complete sentence.*

1) For each of the following questions, decide if the data is *qualitative* or *quantitative*. If it is quantitative, decide if it’s *discrete *or *continuous*. Explain the reason for your answer.

a) Janelle is collecting data on the number of ounces of water drank by college students during a typical math class. What type of data is this?

b) Terrance is collecting data on the color of cars in the school parking lot. What type of data is this?

c) Tina is collecting data on the number of goals scored in college soccer games from around the state. What type of data is this?

2) Describe the difference between qualitative and quantitative data.

3) Describe the difference between discrete and continuous data.

4) Describe the difference between a sampling error and non-sampling error (bias).

5) Give 2 examples of biased sampling.

6) Jenny asks all 75 students in a math course about their score on the midterm. Determine whether this is a population or sample. Describe the parameter and the statistic.

7) Gary surveyed 10 of the 50 people on the top floor and asked them about their favorite flavor of soda. Determine whether this is a population or sample. Describe the parameter and the statistic.

8) Johnny is studying the most commonly purchased vegetables in a small town. He samples the population by dividing the town into blocks and randomly selecting a proportionate number of people from each block. He then collects data from the sample. What type of sampling is used? Explain your answer.

9) Betsy is collecting data on the amount of time shoppers spend inside of a particular large department store. She stands outside the department store and surveys every 10th shopper who exits. What type of sampling is used? Explain your answer.

10) David wants to study the highest level of education for all adults in his city. He sits outside the library and collects data from everyone who enters. What type of sampling is used? Explain your answer.

11) An airline wants to survey some of its passengers to collect data on flight satisfaction. The airline chooses ten flights and surveys every passenger on those flights. What type of sampling is used? Explain your answer.

12) 50 students took a quiz with five questions. The frequency table below shows the results of the quiz. Use the frequency table to answer the following questions.

Value | Frequency | Relative Frequency | Cumulative Frequency |

0 | 4 | 0.08 | 4 |

1 | 8 | 0.16 | 12 |

2 | 6 | 0.12 | 18 |

3 | 2 | 0.04 | 20 |

4 | 15 | 0.3 | 35 |

5 | 15 | 0.3 | 50 |

a) How many students answered exactly 3 questions correctly?

b) How many students answered less than 3 questions correctly?

c) What proportion (percent) of students answered exactly 4 questions correctly?

d) What proportion of students answered 1 or 2 questions correctly?

e) How many students answered at most 4 questions correctly?

f) What is the sum of the relative frequency column? Will this always be the case? Why or why not?

g) Use the data supplied in the frequency table to create a frequency histogram.

13) Describe in one sentence how to calculate the following measures:

a) Mean

b) Median

c) Midrange

d) Variance

e) Standard Deviation

14) What is another word to describe ‘the mean’?

15) Given the following data set, find the mean, median, mode, and midrange.

5, 6, 7, 7, 7, 8, 9, 10

16) Calculate the mean, mode, and midrange from the frequency table given below. Estimate the median.

Value | Frequency |

12 | 9 |

13 | 6 |

14 | 4 |

15 | 7 |

16 | 4 |

17) To find the standard deviation, we start by finding the ______ of the data set. Then, we take each data value and _____ the mean. We will _____ each of these numbers before taking the sum. Once we have added these values, we will _____ by n – 1. Now we have found variance. So, to find the standard deviation, our last step is to take the _____ _____ of the variance.

18) If the given sample variance is 17.56, what is the standard deviation?

19) Find the sample variance and standard deviation of the following set of numbers. The table has been given to you to help with organization. Remember the start by finding the mean.

6, 8, 11, 14, 18

Value | Value – Mean | (Value – Mean)2 |

6 | ||

8 | ||

11 | ||

14 | ||

18 |

The variance of these values is . The standard deviation of these values is .

20) Find the sample variance and standard deviation of the following set of numbers. The table has been given to you to help with organization.

21, 24, 24, 27, 29, 33, 37

Value | Value – Mean | (Value – Mean)2 |

21 | ||

24 | ||

24 | ||

27 | ||

29 | ||

33 | ||

37 |

The variance of these values is . The standard deviation of these values is .

21) In the normal distribution, the mean, median, and mode are _____.

22) For the following two normal curves:

a) Determine the mean of each curve.

b) Which curve has a larger standard deviation? Explain why!

Recall that Z-Score is calculated by where is your score, is the mean, and is the standard deviation. Z-Score tells you have many standard deviations away from the mean you are. Z-scores will almost always fall in between -3 and 3. We then turn this Z-score into a percentile by using a Z-score table, which estimates what percentage of the data our value in question outperforms. You can find complete tables here: http://www.z-table.com/

23) Suppose on a certain MTH 101 quiz, you scored a 94%. The mean score in the class was 82.6% with a standard deviation of 12.4%.

a) How many standard deviations away from the mean are you?

b) Using the following z-table snippet, determine what percent of your classmates you outperformed:

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