Exercises: Data representation

In a first-year ($1º$) secondary school class, a survey was carried out on the students' favorite video game genre. Look at the following bar chart and answer the questions:

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

A group of friends noted down how many pieces of fruit they eat per week. They represented the data in this pictogram, where each fruit symbol 🍎 represents $3$ pieces of fruit eaten.

1. a) How many pieces of fruit did Ana eat in total?
2. b) Who ate exactly $6$ pieces of fruit?
3. c) How many more pieces of fruit than Luis did Sara eat?

Lucía asked her $20$ teammates what their favorite sneaker color was. 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 these data into a frequency table including 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 to represent these results.

The following circle graph represents how the $40$ students in a grade travel to school. Given that half of the class walks, a quarter goes by bus and the rest goes 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 school playground 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 these data using a line graph (frequency polygon) in your exercise book.
2. b) In which one-hour interval did the largest temperature increase occur?
3. c) What was the temperature at ten o'clock in the morning?

Look at this bar chart 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

You can do it on paper and send a photo with your answer.

Match each statistical variable with the type of chart you think is most appropriate to represent it (you may repeat options):

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

2. Eye color of the students in your class.

3. Distribution of a municipality's budget across different areas.

A) Circle graph.

B) Bar chart.

C) Line graph.

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

1. a) If we know that $12$ comics were borrowed, how high 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"? Reason your answer by looking at the chart.

You can do it on paper and send a photo with your answer.

En una clase de $1º$ de secundaria se ha realizado una votación para elegir la temática de la fiesta de fin de curso. Los resultados han sido los siguientes: Superhéroes ($8$ votos), Espacio ($6$ votos), Misterio ($10$ votos) y Deportes ($4$ votos).

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 has 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 (Campsite)	$5$

To represent these data in a circle graph, calculate the angle corresponding to each 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:

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

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

You can do it on paper and send a photo with your answer.

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

Day	Books lent
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.

You can do it on paper and send a photo with your answer.

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

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

2. Calculate the total number of students who took part in the survey.

You can do it on paper and send a photo with your answer.

The following circle graph represents how students at a school manage their free time. Given that the school has $200$ students in total, find out how many students prefer each activity based on the percentages given:

• Video games: $40\%$

• Sports: $30\%$

• Reading: $20\%$

• Music: $10\%$

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

The height of the players on a youth basketball team has been measured (in $cm$). Since the data are very varied, they have been grouped into intervals:

• $[150, 160)$: $4$ players

• $[160, 170)$: $7$ players

• $[170, 180)$: $10$ players

• $[180, 190)$: $3$ players

Represent these data using a histogram. Remember that in a histogram, unlike in a bar chart, the columns are placed right next to each other because the variable is continuous.

You can do it on paper and send a photo with your answer.

Look at the following two graphs. They represent the sales of a sneaker shop in two different months.

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

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

In a survey conducted among the $120$ students of 1st ESO 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 for each sector using the formula: $Ángulo = \frac{f_i}{N} \times 360^\circ$.

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

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

A video game company has recorded how many hours its users play per day. The data have 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.

1. a) Draw the corresponding histogram.

1. b) Next, draw the frequency polygon by joining the midpoints of the top of each bar.

1. c) If the recommended healthy limit is less than $4$ hours, what percentage of users play more than recommended? Round to the nearest tenth.

You can do it on paper and send a photo with your answer.

In an animal shelter, they counted how many bags of food they consume per month. They used this pictogram where each drawing of a "bone" $\square$ represents $15 \text{ kg}$ 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 $0.75 \text{ kg}$ per day, construct a frequency table with the kilograms consumed each month and explain whether in any month the dogs ate less than they need (assume all months have 30 days).

You can do it on paper and send a photo with your answer.

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 are $40$ students in the class in total, build the absolute frequency table and draw the absolute frequency bar chart. What height would the "1 sibling" bar reach on the absolute frequency chart?

You can do it on paper and send a photo with your answer.

Below is a circle graph showing 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 in total took part in the vote?

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

A YouTuber analyses the views of his 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).

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

You can do it on paper and send a photo with your answer.

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

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

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

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