Exercises: Data representation

In a $1º$ class, a survey was conducted on the students' preferred video game genre. Look at the following bar graph and answer the questions:

1. a) Which video game genre do the students like the most (the mode)?
2. b) How many students prefer adventure games?
3. c) If we add up all the answers, how many students participated in the survey?

A group of friends recorded how much fruit they eat per week. They represented the data in this pictograph, where each fruit symbol 🍎 represents $3$ pieces of fruit eaten.

1. a) How many pieces of fruit has Ashley eaten in total?
2. b) Who has eaten exactly $6$ pieces of fruit?
3. c) How many more pieces of fruit has Sarah eaten than Lucas?

Chloe asked her $20$ teammates what their favorite sneaker color is. The results were:

Red, Blue, Blue, White, Red, White, White, Blue, Red, White, Blue, Blue, White, Red, White, White, Blue, White, Blue, White.

1. a) Organize this data into a frequency table that includes the color and the absolute frequency ($f_i$).
2. b) What is the mode of this study?
3. c) Draw a simple bar graph in your notebook representing these results.

The following circle graph represents how the $40$ students in a grade travel to school. Knowing that half the class walks, a quarter takes the bus, and the rest go by car:

1. a) How many students walk to school?
2. b) How many students go by bus?
3. c) What angle in degrees corresponds to the sector of students who walk? (Remember that a full circle is $360^\circ$).

The following table shows the temperature recorded in the schoolyard over five hours on a winter morning:

Time	$8:00$	$9:00$	$10:00$	$11:00$	$12:00$
Temp. ($^\circ C$)	$4$	$6$	$9$	$12$	$11$

1. a) Represent this data using a line graph (frequency polygon) in your notebook.
2. b) In which one-hour interval did the greatest temperature increase occur?
3. c) What was the temperature at ten in the morning?

Look at this bar graph about the number of siblings of the students in a class and complete the frequency table below:

No. of siblings	Absolute frequency ($f_i$)
$0$
$1$
$2$
$3$ or more
Total

Match each statistical variable with the type of graph you think is most suitable to represent it (you can repeat options):

1. Changes in a baby's height month by month.

2. Eye color of the students in your class.

3. Distribution of a city budget across different areas.

A) Circle graph.

B) Bar graph.

C) Line graph.

In a library, they counted how many books of each type were borrowed in a day. They have started to draw the bar graph, but the last column is missing.

1. a) If we know that $12$ comic books have been borrowed, up to what height should the "Comic" bar reach on the vertical axis?
2. b) Which type of book has been borrowed the least so far?
3. c) Is "Poetry" the mode? Justify your answer by looking at the graph.

In a $1º$ middle school class, a vote was held to choose the theme for the end-of-year party. The results were as follows: Superheroes ($8$ votes), Space ($6$ votes), Mystery ($10$ votes), and Sports ($4$ votes).

Calculate the relative frequency of each option and represent the data in a bar chart. Make sure the vertical axis is correctly scaled and labeled.

A group of friends wants to organize a trip and they have asked $40$ classmates about their preferred destination. The results are shown in the following table:

Destination	Absolute Frequency ($f_i$)
Beach	$15$
Mountains	$10$
European City	$10$
Adventure (Camping)	$5$

To represent this data in a pie chart, calculate the angle corresponding to each circular sector. Remember that the total sum of the angles must be $360^\circ$.

The number of hours that $20$ teenagers spend doing sports per week has been recorded:

$2, 4, 3, 5, 2, 6, 4, 3, 3, 5, 4, 2, 6, 3, 4, 5, 2, 3, 4, 3$.

Construct the absolute frequency table and represent the data using a frequency polygon. What trend do you observe in the graph?

In the school library, they want to visualize how many books have been borrowed each day of the week. They have decided to use a pictogram where each "book" symbol represents $5$ loans.

Day	Books borrowed
Monday	$20$
Tuesday	$15$
Wednesday	$25$
Thursday	$10$
Friday	$30$

Draw the corresponding pictogram in your notebook using a simple symbol to represent the books. Calculate how many symbols you need for each day.

From the following bar chart about the number of pets the students in a class have, carry out the reverse process:

1. Create the frequency table (absolute and relative).

2. Calculate the total number of students who participated in the survey.

The following pie chart represents how the students of a school manage their free time. If we know that the school has $200$ students in total, find out how many students prefer each activity based on the percentages indicated:

• Video games: $40\%$

• Sports: $30\%$

• Reading: $20\%$

• Music: $10\%$

Reproduce it in your notebook by calculating the degrees of each sector.

The height of the players on a youth basketball team has been measured (in $cm$). As the data is very varied, it has been grouped into intervals:

• $[150, 160)$: $4$ players

• $[160, 170)$: $7$ players

• $[170, 180)$: $10$ players

• $[180, 190)$: $3$ players

Represent this data using a histogram. Remember that in a histogram, unlike a bar graph, the bars touch each other because the variable is continuous.

Look at the two graphs below. They represent the sales of a sneaker store in two different months.

1. Which of the two graphs could be misleading or give a false impression that sales have grown enormously?

2. Look at the vertical axis. Do they both start at zero? Explain why it is important that statistical axes are not "truncated."

In a survey of $120$ 6th grade students about their favorite streaming platform, the following results were obtained: $40\%$ prefer Netflix, $30$ students choose Disney+, the relative frequency of HBO is $0,15$, and the rest opt for Twitch.

Calculate the absolute frequency of each category and draw a pie chart. To do this, you must indicate the exact angle in degrees of each circular sector using the formula: $Ángulo = \frac{f_i}{N} \cdot 360^\circ$.

A group of scientists is measuring the growth of a plant under a new LED light. Over 6 weeks, the height in inches has followed this progression: $2, 5, 9, 14, 20, 27$.

Represent this data in a line graph. Then, add a second line (in a different style or color) representing the "ideal height" if the plant grew exactly $4 \text{ in}$ per week (starting from the initial $2 \text{ in}$). In which week is the difference between the real and ideal plant the greatest?

A video game company has recorded how many hours its users play per day. The data has been grouped into the following intervals: $[0, 2)$, $[2, 4)$, $[4, 6)$, and $[6, 8)$. The absolute frequencies are $25, 40, 15$ and $10$ respectively.

Draw the corresponding histogram. Next, draw the frequency polygon by joining the midpoints of the top of each bar. If the recommended healthy limit is less than $4$ hours, what percentage of users play more than the recommended amount?

An animal shelter has counted how many bags of food they consume per month. They have used this pictogram where each drawing of a "bone" $\square$ represents $15 \text{ lb}$ of food.

• January: $\square \square \square \square$

• February: $\square \square \square$

• March: $\square \square \square \square \square$

Knowing that the shelter has $30$ dogs and that each dog should eat $0,75 \text{ lb}$ a day, construct a frequency table with the pounds consumed each month and explain if in any month the dogs have eaten less than they need (assume all months have 30 days).

A study has been carried out on the number of siblings of the students in a class. The relative frequency bar chart shows that:

• $20\%$ have no siblings.

• $50\%$ have 1 sibling.

• $25\%$ have 2 siblings.

• The rest have 3 siblings.

If there is a total of $40$ students in the class, construct the absolute frequency table and draw the absolute frequency bar chart. What height would the "1 sibling" bar reach on the absolute frequency chart?

Below is a pie chart of the results of a vote to choose the color of the graduation T-shirt (Blue, Red, Green). The Blue sector measures $144^\circ$ and the Red sector measures $108^\circ$.

1. Calculate the angle of the Green sector.

2. If we know that $30$ people voted for the color Red, how many people participated in the vote in total?

3. Calculate the absolute frequencies of the other two colors and represent the final results in a bar chart.

A YouTuber analyzes the views of their latest video. In the first 4 hours, the cumulative views were:

• Hour 1: $150$ views.

• Hour 2: $400$ views (in total).

• Hour 3: $750$ views (in total).

• Hour 4: $900$ views (in total).

Construct a table that differentiates between the absolute frequency (new views each hour) and the cumulative frequency. Represent the new views for each hour in a bar chart. In which hour was there the greatest success in attracting new viewers?

Compare the following two sets of data on the mean temperature ($^\circ\text{C}$) recorded at noon over a week in two different cities:

• City A: $12, 14, 15, 12, 11, 13, 14$

• City B: $18, 17, 19, 18, 20, 19, 18$

Represent both cities on the same line graph (use two different colors or line styles). Calculate the mean temperature of each city and draw a dotted horizontal line representing the mean of City B. Which of the two cities has more stable temperatures (smaller range)?