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Step $1$	Determine the center (median) by finding the middle data point.
Step $2$	Find the maximum and minimum values on the graph. Use these values to calculate the spread (range) of the data.
Step $3$	Analyze the overall shape of the graph. Note any other features of interest on the graph.

Complete each step one at a time.

Step $1$

First, the total number of data points should be found. This is why begin by counting all the dots in the given dot plot.

There are $15$ data points. This means that there were $15$ participants in the math competition that obtained a grade. The median of the data set is, therefore, the $8\text{th}$ data point, as it divides the set into halves. Find its value on the dot plot.

The $8\text{th}$ data point is $6,$ which means that the median or the center of the data set is $6.$ This measure indicates the middle value of all the grades obtained by the participants.

Step $2$

Now, find the maximum and minimum values on the dot plot.

The minimum grade obtained by a participant is $2$ and the maximum grade is $10.$ To find the range, calculate the difference between these values. This means that the range of grades obtained by the participants of the math competition is $8.$

Step $3$

The next step is to analyze the overall shape of the graph.

The overall shape of this graph appears to be the bell shape of a normal distribution, meaning the grades are overall normally distributed, and the plot is symmetric in shape.

Step $1$	Draw a horizontal line to begin the dot plot. Title the dot plot based on the problem, and label the plot with the categories/numbers. When labeling the line with numbers, the numbers must be sequential and in a consecutive order.
Step $2$	Determine the frequency for each piece of data provided in the problem.
Step $3$	Place dots over each category or number on the horizontal line that corresponds to the frequency for each piece of data as depicted in the table.

Complete each step one at a time.

Step $1$

First, a horizontal line should be drawn. The given data set includes the grades of the participants from last year, so the title of the dot plot can be Grades From Last Year. Also, the grades vary from $1$ to $9,$ so the dot plot can be labeled with the consecutive integers from $1$ to $9.$

Step $2$

The next step is to determine the frequency of each grade obtained by the participants from last year's math competition. To do so, count how many times each grade from $1$ to $9$ appears and write that number in a table next to the grade.

Grade	Frequency
$1$	$1$
$2$	$0$
$3$	$1$
$4$	$2$
$5$	$0$
$6$	$3$
$7$	$3$
$8$	$2$
$9$	$1$

Step $3$

Lastly, place dots over each grade from $1$ to $9$ the number of times it appears in the data set. Use the values from the frequency table.

This way the dot plot for the given data set of values was formed.

Step $1$	Identify the independent and dependent variable.
Step $2$	List the frequency in each bin.
Step $3$	Interpret the data and describe the bar graph's shape. Use the interpretation to answer any questions about the data.

Complete each step one at a time.

Step $1$

First, the independent and dependent variables need to be identified. The horizontal line lists days of a week while the vertical line represents the number of tickets sold.

The article analyzes how many tickets are sold on different days of a week and which day has the most sales. This means that the independent variable is the days of the week and the dependent variable is the number of tickets sold on each day.

Step $2$

Next, the frequency in each bin should be listed and interpreted. Use the values given in the bar graph to indicate the height of each bin. Remember that the vertical line represents the number of tickets sold on each day.

Day	Frequency
Monday	$64$ tickets were sold.
Tuesday	$70$ tickets were sold.
Wednesday	$62$ tickets were sold.
Thursday	$137$ tickets were sold.
Friday	$295$ tickets were sold.
Saturday	$342$ tickets were sold.
Sunday	$260$ tickets were sold.

Step $3$

Lastly, interpret the data and describe the bar graph's shape. The bar graph shows that the distribution of ticket sales is left-skewed.

Friday and Saturday are the days with the most number of tickets sold, $295$ and $342$ respectively. Also, the largest number of tickets tend to be sold on Saturday, and that number of tickets is $342.$

Step $1$	Choose the number of intervals
Step $2$	Determine the size of the intervals
Step $3$	Make a frequency table
Step $4$	Draw a histogram

Complete each step one at a time.

Step $1$

The first step is determining what intervals of numbers it will have. Remember that each interval must have the same length and all data points must lie in an interval. First, count the numbers in the data set. To find a suitable number of intervals, take the square root of the number of data points. In this case, there are $30$ data points. This means that the histogram can have either four or five intervals. In this case, it will have four intervals.

Step $2$

Next, the size of the intervals needs to be determined. This can be done by identifying the lowest and highest data value in the set. Since the lowest data value in the set is $7$ and the highest is $70,$ using four intervals with a range of $20$ will cover numbers from $1$ to $80$ and, therefore, will encompass all data points. The intervals of the histogram will be the following.

Step $3$

The next step is to make a frequency table showing how many data points lie in each interval.

Interval	Data Points	Frequency
$1-20$	$7,$ $9,$ $11,$ $13,$ $15,$ $17,$ $18,$ $19,$ $20$	$9$
$21-40$	$21,$ $22,$ $23,$ $24,$ $24,$ $24,$ $25,$ $26,$ $27,$ $28,$ $30,$ $32,$ $35,$ $37,$ $39$	$15$
$41-60$	$42,$ $45,$ $49,$ $55,$ $60$	$5$
$61-80$	$70$	$1$

Step $4$

From the frequency table, the histogram can be constructed by drawing a bar over each interval with a height corresponding to the found frequency.

Recall what each part of a box plot represents.

Now, consider the given box plot.

By comparing the general box plot with this one, the minimum, maximum, median, first and third quartiles can be determined. Next, use the definitions of each concept to see what each of these values mean.

Concept	Value	Meaning
Minimum	$24$	The least level of pollution in the analyzed areas is $24$ out of $100.$
Maximum	$98$	The greatest level of pollution in the analyzed areas is $98$ out of $100.$
Median	$63.5$	The average level of pollution in the analyzed areas is $63.5$ out of $100.$
First Quartile	$39$	$25\%$ of the analyzed areas have the level of pollution at $39$ or less.
Third Quartile	$83$	$25\%$ of the analyzed areas have the level of pollution at $83$ or more.

Step $1$	Order the data set from least to greatest value. Find the minimum and maximum.
Step $2$	Determine the median.
Step $3$	Determine the first and third quartiles.
Step $4$	Draw a box plot.

Complete each step one at a time.

Step $1$

Begin by ordering the given data set from least to greatest value. Now the minimum and maximum are easily identifiable in this ordered data set. Here, the minimum is $7$ and the maximum is $71.$

Step $2$

To find the median of the data set, the number of values in the set should first be determined. Begin by counting all the data points. To find the median, look for the value that lies in the middle of a data set. Since there are $20$ values, the median is the mean of the numbers at the $10\text{th}$ and $11\text{th}$ position. Now, determine the median by calculating the mean of $36$ and $38.$ The median is $37.$

Step $3$

The next step is to find the first and third quartiles of the data set. The median divides the set into two smaller sets, each with $10$ values. The first quartile is the mean of the $5\text{th}$ and $6\text{th}$ value in the first set with smaller values. It equals $20.$ The third quartile is the median of the second set with greater values. It can be calculated as a mean of the $15\text{th}$ and $16\text{th}$ value. Its value is $53.5.$

Step $4$

To draw a box plot, recall the found values of the minimum, maximum, median, first and third quartiles of the data set. First, mark the values of minimum and maximum above a number line with a line segment, indicating the range of the box plot.

Next, mark the median as a vertical line segment in the range above the number line. Remember that the line for the median falls inside the box.

The first and third quartiles are marked as the left and right sides of the box plot. The box plot can be completed by drawing a box between the quartiles.

The data is evenly distributed between the left and right side, so it is a symmetric distribution. It only has one cluster of data values within the interval $1-8$ and there are no gaps. The value $5$ is a peak because it is the most frequently occurring value.

Next, decide which measures of center and spread are the most appropriate based on the symmetry of the distribution. Remember what measures can be used in this situation.

Symmetric Distribution?	Measure of Center	Measure of Spread
Yes	Mean	Mean absolute deviation
No	Median	Interquartile range

Since this distribution is symmetric, it is best to use the mean as a measure of center and the mean absolute deviation as the measure of spread.

Here, the left side of the data is different than the right side, so the distribution is not symmetric. Also, there are two clusters of data values within the intervals $17-20$ and $22-24$ separated by a gap at $21.$ The peak of the data set is at $23.$

The most appropriate measures of center and spread can be determined by looking at the symmetry of the distribution. When the distribution is not symmetric, as in this case, it is best to use the median as a measure of center and the interquartile range as the measure of spread.

Hour	Distance Traveled, (mi)
$1$	$70$
$2$	$135$
$3$	$203$
$4$	$278$
$5$	$348$

The distance data includes values from $70$ to $348,$ so a scale from $0$ to $420$ miles with an interval of $70$ miles are reasonable. The horizontal axis can represent time in hours and the vertical axis can represent the distance traveled in miles. Now, the points can be plotted on a coordinate plane and connected.

This way the line graph representing the distance traveled by Tadeo's family to his grandparents was made.

Notice that the graph shows an upward slant of the line with a steady increase from hours $1$ to $5.$ To predict in how many hours Tadeo will reach his grandparents, extend the graph to the point where the distance is $420$ miles following the trend from the graph.

It can be predicted that Tadeo's family will reach their destination after about $6$ hours of traveling.

Type of Display	Best Used to
Bar Graph	It shows the number of items in specific categories.
Box Plot	It shows measures of variation for a set of data. It is also useful for very large data sets.
Histogram	It shows the frequency of data divided into equal intervals.
Line Graph	It shows the change over a period of time.
Line Plot	It shows how many times each number occurs.

The given data set lists the countries and the corresponding life expectancy. After analyzing the available types of displays, a bar graph looks like the best choice as it can show the data in two categories: country and life expectancy.

Country	Life Expectancy
United States	$76.3$
Japan	$84.5$
Germany	$80.9$
Brazil	$77.3$
China	$78.2$
India	$68.3$
Australia	$83.3$
South Africa	$62.4$

The countries can be marked on the horizontal axis and the life expectancy can be marked on the vertical axis. Next, draw bars with the height equal to the life expectancy.