Box Plots
Comparing Data Sets
Types of Studies
Types of Sampling
Miscellaneous
100
Given the following data set:
3,7,5,10,9,12,8,14,18,15
Draw the box plot for this data. Indicate the minimum, Q1, median, Q3, and maximum values.
Min: 3
Q1: 7
Med: 9.5
Q3: 14
Max:18
100
The following two data sets represent the number of hours spent studying by two students during a week:
- Student A: 2, 4, 5, 6, 6, 7, 8
- Student B: 3, 4, 5, 6, 7, 7, 9
a) Find the mean of both data sets.
b) Which student spent more time studying on average?
Student A: 5.43
Student B: 5.86
Student B spent more time studying on average
100
A researcher wants to study the correlation between screen time and sleep quality in teenagers, so she goes and shadows the daily habits of teenagers in different cities.
Which type of statistical study is being used?
Observational Study
100
A researcher randomly selects 50 citizens from a list of all residents in Chocowinity to ask about their eating habits. What type of sampling is this?
Simple Random Sampling
100
Separate this list into two groups: categorical data and quantitative data
marathon time
marital status
level of education received
gender
goals scored in a soccer match
year
class rank
height
temperature
Categorical Data:
gender, year, class rank, marital status, education level
Quantitative Data:
height, temperature, goals scored, marathon time
200
For the following data set:
1,22,7,8,14,19,2,10,6,11,15,19,25
a) Find the first quartile (Q1), third quartile (Q3), and the interquartile range (IQR).
Q1:6.5
Q3:19
IQR:12.5
200
You are given two histograms that represent the scores of two classes on a quiz:
James Charles's Class: The scores are grouped into bins:
0−10:4 students, 10−20:5 students, 20−30:8 students, 30−40:1 studentJojo Siwa's Class: The scores are grouped into bins:
0−10:2 students, 10−20:6 students, 20−30:5 students, 30−40:5 students
Compare the central tendency (mean/median) and spread of the two distributions.
a) Which class appears to have a higher concentration of higher scores?
Jojo Siwa's Class
200
A pharmaceutical company conducts an experiment where one group of patients receives a new medication, while another group receives a placebo. After a month, the company compares the health outcomes between the two groups.
Which type of statistical study is being used?
Experimental Study
200
A principal divides a high school into groups based on grade level (9th, 10th, 11th, and 12th) and then selects 10 students from each grade to participate in a survey about extracurricular activities. What type of sampling is this?
Stratified Sampling
200
Is there bias in this study? If so, what is wrong with this study?
A grocery store manager wants to understand customer preferences, so they conduct a survey in the organic food section of the store.
Yes, the researcher only conducted the survey in the organic food section.
300
Two box plots represent the scores of two classes on the same final exam:
- Class A: Minimum = 45, Q1 = 60, Median = 75, Q3 = 85, Maximum = 95
- Class B: Minimum = 50, Q1 = 65, Median = 70, Q3 = 80, Maximum = 90
a) Create a box plot and compare the spread of the two classes' scores.
b) Based on the box plots, which class performed better overall?
Class A
300
Two students, A and B, recorded their daily workout times (in minutes) for a week:
- Student A: 30, 32, 33, 34, 31, 30, 33
- Student B: 28, 35, 30, 32, 31, 29, 36
a) Calculate the standard deviation for both data sets.
b) Which student had more consistency in their workout times?
Student A: 1.45
Student B: 2.76
Student A has a lower standard deviation so Student A was more consistent in their workouts
300
Which type of study would you use if you wanted to research consumer preference on a new product?
Survey
300
A marketing firm conducts a study by selecting every 5th person who enters a shopping mall on a given day to complete a survey. What type of sampling is used?
Systematic Sampling
300
Is there bias in this study? If so, what is wrong with this study?
A researcher wants to study the effects of a new diet and recruits participants who are members who workout regularly.
Yes, because people who workout regularly are generally more health-conscious and motivated which could skew the results.
400
The box plot below represents the monthly incomes (in thousands) of employees at a large company:
- Minimum = 2
- Q1 = 4
- Median = 6
- Q3 = 8
- Maximum = 16
a) Describe the skewness of the distribution.
b) What do you infer about the income distribution at the company based on the shape of the box plot?
a) left skewed
b) Most people get around 4-8 thousand a month
400
The distribution of cat ownership is symmetric while the distribution for dog ownership is skewed right.
400
Which study do you need to use to study the long-term effects of air pollution on public health?
Observational Study
400
To understand consumer preferences in a city, a researcher divides the city into neighborhoods and randomly selects 3 neighborhoods. They then survey every resident in those neighborhoods. What type of sampling is this?
Cluster Sampling
400
Is there bias in this study? If so, what is wrong with this study?
A researcher wants to determine the average time high school students spend on homework each night. They obtain a list of all students at the school and randomly select 150 students. These students are asked to record the time they spend on homework each night over a week, and the data is then averaged.
No, this study does not have any bias
500
A researcher collects the following data for the number of hours of sleep per night (rounded to the nearest hour) for a group of 20 students:
5,7,8,9,10,13,5,6,7,8,5,7,8,9,6,7,10,6,8, 3
Construct a box plot for the data and answer the following questions:
a) Identify any potential outliers
b) What conclusions can you draw from the box plot about the sleep habits of this group of students?
a) Outlier is 13
b) most students get on average 7-8 hours on sleep
500
1-B
2-C
3-A
500
Which study would you use if you wanted to research mental health and stress levels in college students?
Survey
500
Ms. Petty wants to know the average time students study every night. So, she asks every student in her class and records the data. What type of sampling is this?
Convenience Sample
500
Is there bias in this study? If so, what is wrong with this study?
A political poll is conducted by calling landline phone numbers during weekday afternoons to gauge opinions about an upcoming election.
Yes, the poll may underrepresent younger voters or those who work during the day and may not own landlines.