MTH 101Organizing Data
Define the following terms.
1. Frequency – the count of how many times a particular date value appears in the data set.
2. Frequency Table – constructed by arranging the data in order from least to greatest with their
corresponding frequencies
3. Relative Frequency – a how many times a frequency is shown up on the data set of the total
number of the value
4. Cumulative Frequency – the accumulation of previous frequencies
5. Histogram – is graph that consist of contiguous (adjoining) box, and can show you the shapes o,
the center, and the spread of the data.
6. Stem and Leaf Plot – Each data value will be separated into stem and a leaf, using its digits. The
“leaf” consists of a final significant digit. The stem contains the remaining digit in front of the
“leaf”
Use your knowledge of these terms to answer the following questions.
1.) 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
MTH 101
5
15
0.3
50
a.) How many students answered 3 questions correctly? 2
b.) How many students answered less than 3 questions correctly? 18
c.) What proportion of students answered 4 questions correctly? 15
d.) What proportion of students answered 1 or 2 questions correctly? 14
e.) How many students answered at most 4 questions correctly? 30
f.) What is the sum of the relative frequency column? Will this always be the case? Why or why not? I
don’t think it will always be same because the values can differentiate.
2.) Use the data supplied in the frequency table to create a frequency histogram.
‘Frequency’
16
14
Frequency
12
10
8
6
4
2
0
0
1
2
3
4
5
Value
3.) A group of high school seniors were asked how many hours of sleep they get per night. Below is
their response. Use this data to create a frequency table, and include relative and cumulative
MTH 101
frequency as well. Upon completion of the table, create a frequency and relative frequency histogram.
Use the table and histograms to answer the following questions.
4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7,7 8, 8, 9
a.) How many students get at least the recommended eight hours of sleep?
b.) How many students get less than seven hours of sleep?
c.) How many students get exactly five hours of sleep?
d.) What proportion of students get less than the recommended eight hours of sleep?
e.) What proportion of students get seven or eight hours of sleep?
f.) What is similar about the frequency histogram and the relative frequency histogram?
g.) What is different about the frequency histogram and the relative frequency histogram?
4.) The same group of seniors displayed their last math exam scores. Display these results in a stem
and leaf plot.
42, 47, 56, 58, 61, 63, 68, 74, 75, 79, 79, 80, 82, 83, 87, 87, 87, 87, 89, 90, 92, 92, 94, 99, 100
MTH 101
Data Basics
Define the following terms:
1.
2.
3.
4.
5.
Qualitative data: are results
Quantitative data: are measuring or counting of population( always in numbers)
Discrete data: are all datas which result in counting
Continuous data: Are assumptions that you are measuring accurately
Sampling errors: sampling will never be exactly representative of the population, The sample
you choose may not be larger enough to show true information
6. Nonsampling errors: which are caused by things that are not related to sampling process
a. Random error
b. Systematic error is and error which is made bais measurement leading to many
separate measures which differentiates widely from actually value
7. Bias: where some members are are not likely o choose as others
8. Inferential statistics :helps create a better understanding of data. Also produces data for
generalizing populations by using various tools and tests. Work with a sample to make
generalizations of a test.
9. Population. U.s Census
10. Sample
11. Parameter A parameter of interest is what your data is focused on.
12. Statistic: a fact or piece of data from a study of a large quantity of numerical
data:”the statistics show that the crime rate has increased”
13. Data
14. Variable: able to adapt to changes
Types of Sampling: (15 – 18)
1.) Stratified: overlapping of population, this occurs when a population splits up into two
2.) Cluster: Is used to collect data by using simple random samples of truly populated groups
Systematic: A systematic sample is obtained by a very straight forward process:
1.
2.
Begin with a positive whole number k.
Look at our population and then select the kth element.
MTH 101
3.
4.
5.
Select the 2kth element.
Continue this process, selecting every kth element.
We stop this selection process when we have reached the desired number of elements in our
sample.
3.) Convenience: being able to access something easily
Use your knowledge of the terms above to answer the following questions:
1.) 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?
A) Qualitative data
B) Discrete quantitative data
C) Continuous quantitative data
D) None of the above
2.) Terrance is collecting data on the color of cars in the school parking lot. What type of data is this?
A) Qualitative data
B) Discrete quantitative data
C) Continuous quantitative data
D) None of the above
3.) Tina is collecting data on the number of goals scored in college soccer games from around the
state. What type of data is this?
A) Qualitative data
B) Discrete quantitative data
C) Continuous quantitative data
D) None of the above
4.) Describe the difference between qualitative and quantitative data.
Qualiative date is descriptive information and Quantitative data is numerical information
5.) Describe the difference between discrete and continuous data.
Discrete data is counting and deals with whole numbers and continuous data is results is measures.
MTH 101
6.) Describe the difference between a sampling error and nonsampling error.
Non sampling error is interpreted / sampling error
7.) Describe the difference between the two types of no sampling error, random error and systematic
error.
Systematic error is in the sampling error and random error is non sampling error.
8.) Give 2 examples of a bias sampling.
Choosing car insurance with roadside assistance over insurance that doesn’t provide it
9.) Give an example when you may use inferential statistics.
10.) Jenny asks all 75 students in a math course about their score on the midterm. Determine whether
this is a population or sample and next describe the parameter or statistic.
11.) 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 and next describe the parameter or statistic.
12.) 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?
13.) 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?
14.) 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?
MTH 101
15.) 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?
16.) List at least 3 ways statistics can be misleading.
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