Exercises: Representing the data

In a 2nd ESO class, a survey was conducted to find out the students' favorite social network. The following results were obtained: Instagram, TikTok, TikTok, YouTube, Instagram, TikTok, YouTube, Instagram, Instagram, TikTok, YouTube, TikTok, Instagram, YouTube, Instagram.

State the population of this study, the individual, and the type of statistical variable.

Look at the following bar chart representing the favorite sport of a group of teenagers from a sports club:

Using the graph, answer the following:

1. a) How many people prefer basketball?
2. b) Which sport is the least practiced in this group?
3. c) How many people were surveyed in total?

Students in a class were asked for the number of siblings they have, obtaining the following data:

$1, 0, 2, 1, 1, 0, 3, 2, 1, 1, 0, 2, 1, 4, 1, 0, 2, 1, 1, 2$

Construct a frequency table including the absolute frequency ($n_i$) and the relative frequency ($f_i$).

To represent the results of a survey about preferred ice cream flavors on a circle graph, we need to calculate the angles for each section. If we know that $10$ out of a total of $40$ people like chocolate, what angle size in degrees ($^\circ$) will the sector corresponding to chocolate have?

The following pictogram shows the number of trees planted by the students of a middle school over four years. If each symbol represents $5$ trees, answer the following questions:

1. a) How many trees were planted in the year $2021$?
2. b) In which year were exactly $15$ trees planted?
3. c) What is the total number of trees planted over the four years?

The time (in minutes) taken by $25$ students to get to school from home has been recorded. The data has been grouped into the following table of intervals:

Represent these data using a histogram. (Remember to place the intervals on the horizontal axis and the frequencies on the vertical axis).

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

The following line graph shows the evolution of the maximum temperature in a city during the first week of May:

Looking at the graph:

1. a) On which day of the week was the highest maximum temperature recorded?
2. b) Between which two consecutive days was there the greatest drop in temperature?
3. c) What was the maximum temperature on Monday?

A video game company wants to find out how many hours a week young people aged $12$ to $14$ spend playing video games. They surveyed $100$ boys and girls chosen at random from different secondary schools in Mexico.

In this case, identify:

1. a) What is the population?
2. b) What is the sample?
3. c) What is the individual?
4. d) Is it a qualitative or quantitative variable?

In a study on social media use, $40$ teenagers at a middle school were asked about their favorite platform. The results obtained are as follows:

• TikTok: $18$ people.

• Instagram: $12$ people.

• YouTube: $6$ people.

• BeReal: $4$ people.

1. a) Identify the population, sample, and type of statistical variable.
2. b) Draw up a frequency table including the frequency ($n_i$), relative frequency ($f_i$), and percentage ($\%$) for each value.
3. c) Represent the data on a bar chart.

The number of books read by students in a 2nd ESO class during the first term was recorded. The data are:

$1, 2, 0, 3, 1, 1, 2, 0, 1, 4, 2, 1, 1, 0, 2, 3, 1, 2, 1, 0, 5, 2, 1, 2, 1$.

1. a) Draw up the table of frequencies and cumulative frequencies ($N_i$).
2. b) What percentage of students read $2$ books or fewer?
3. c) Draw a frequency polygon over the bar chart of the frequencies.

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

A video game company wants to represent the type of console preferred by visitors at a gaming convention in a circle graph. The data are:

• PlayStation: $45\%$

• Nintendo Switch: $30\%$

• Xbox: $15\%$

• PC: $10\%$

1. a) Calculate the degrees corresponding to each circular sector using proportion or the sector angle formula: $\alpha = \frac{360^\circ \times n_i}{N}$.
2. b) Draw an approximate circle graph using the calculated angles.

The height (in cm) of the $20$ members of a youth basketball club was measured. Being a continuous variable, the data have been grouped into the following intervals:

$[160, 165), [165, 170), [170, 175), [175, 180), [180, 185]$.

The frequencies are: $2, 5, 8, 3, 2$, respectively.

1. a) State the class marks ($x_i$) for each interval.
2. b) Represent the data on a histogram. Explain how this graph differs from a conventional bar chart.
3. c) What is the modal class?

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

The municipality of a town wants to raise awareness about recycling. To do so, it has published a pictogram showing the number of recycling bins installed in four different neighborhoods.

If each ♻️ symbol is equivalent to $12$ bins:

• Neighborhood A: ♻️♻️♻️♻️

• Neighborhood B: ♻️♻️♻️

• Neighborhood C: ♻️♻️♻️♻️♻️

• Neighborhood D: ♻️♻️

1. a) Construct the frequency table for the number of bins in each neighborhood.
2. b) What is the total number of bins installed in the town?
3. c) Represent these same data using a bar graph to compare both visual methods.

Look at the following two graphs showing the change in average temperature in a city during a spring morning. Both represent the same data, but have been drawn with different scales on the vertical axis.

1. a) Explain why Graph B gives the impression of much faster growth than Graph A if the data are identical.
2. b) Which of the two graphs do you think is more objective for informing the public? Reason your answer based on the scale of the vertical axis.

A climate graph (climograph) is a graph that combines a bar graph (rainfall) and a line graph (temperature). Look at the simplified data for a quarter in a city in southern Mexico:

• January: $10^\circ C$, $60\text{ mm}$

• February: $12^\circ C$, $45\text{ mm}$

• March: $15^\circ C$, $30\text{ mm}$

1. a) Draw the climate graph, placing the months on the $X$ axis, rainfall on the left $Y$ axis (bars), and temperatures on the right $Y$ axis (line).
2. b) By analyzing the graph, what trend do you observe moving from winter to spring?

A survey was conducted among $120$ people about their weekly physical activity. The results are presented in this incomplete table:

1. a) Complete all the gaps in the table knowing that the total number of individuals ($N$) is $120$.
2. b) Represent the data in a circle graph.
3. c) State the mode of this study.

An e-sports club has carried out a study on the number of hours per week that its $120$ members spend training. We have the following partial data from the frequency table, where the data have been grouped into intervals of the same width:

Complete the frequency table and represent the data using a histogram with a frequency polygon superimposed on it. State what percentage of members train $10$ hours or more per week.

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

A phone company analyses the battery life of two smartphone models, A and B, after one year of use. The results are shown in the following box plot (box-and-whisker plot). Look at the graph and answer:

1. a) What is the median duration for each model?
2. b) If a user needs the battery to last at least $18$ hours, which model has a higher proportion of devices that meet this requirement? Justify your answer using the quartiles.
3. c) Which of the two models has a more spread-out distribution in the central $50\%$ of the data?

An influencer wants to show the growth of their followers on two different social networks during the last six months. To do so, they present the following graphs.

1. a) Explain why the graph for Social Network Y could be misleading to sponsors if they do not look at the vertical axis.
2. b) Knowing that on Social Network X they started with $10,000$ followers and ended with $12,000$, and on Social Network Y they started with $50,000$ and ended with $51,000$, draw a single comparative line graph using an appropriate scale that allows for comparing the actual growth of both accounts.

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

The municipality of a town collected data on household organic waste recycling from $200$ families. The following circle graph shows the distribution, but the data for families who recycle "A lot" have been erased.

• None ($0$ kg/month): $15\%$

• A little ($1-5$ kg/month): $72^\circ$ (sector angle)

• Moderate ($6-10$ kg/month): $90$ families

• A lot ($>10$ kg/month): $?$

1. a) Calculate the number of families belonging to each category.
2. b) Calculate the angle in degrees of the sector corresponding to families who recycle "A lot".
3. c) Make a frequency and relative frequency table with all the data.

In a study on school library usage, the number of books borrowed by a sample of 2nd ESO students during a term was recorded. The results are shown in the following cumulative frequency bar chart ($N_i$):

1. a) How many students make up the sample?
2. b) Construct the frequency table ($n_i$) from the cumulative frequencies.
3. c) What are the mode and the median of the number of books borrowed?
4. d) Represent the data using a pie chart.

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

A survey was carried out among $400$ teenagers about their favorite weekend activity, distinguishing between boys and girls. The data are shown in the following two-way table, but some values are missing:

1. a) Complete all the missing values in the table.
2. b) Represent the data using a grouped bar graph (one bar for boys and one for girls for each activity).
3. c) What percentage of girls prefer sports? Is it higher or lower than the percentage of boys who prefer sports?

The reaction time (in seconds) of a group of athletes to the starting signal is represented in the following histogram. The intervals are of the form $[a, b)$.

1. a) Calculate the total number of athletes who took part in the race, knowing that there were $12$ athletes in the interval $[0,15, 0.20)$.
2. b) Calculate the class mark for each interval.
3. c) Estimate the mean reaction time from the histogram data.
4. d) What percentage of athletes have a reaction time of less than $0.20$ seconds?

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

An NGO conducted a survey on the number of children in $50$ families in a neighborhood. The results have been lost, but we still have the pictogram where each house symbol represents $4$ families.

• $0$ children: $\triangle \triangle \triangle$

• $1$ child: $\triangle \triangle \triangle \triangle \triangle$

• $2$ children: $\triangle \triangle \triangle \triangle$

• $3$ children or more: $?$

1. a) Knowing that the total number of families is $50$, how many families have $3$ children or more? How would you represent that amount on the pictogram?
2. b) Calculate the mean, median, and mode of the distribution.
3. c) If a family is chosen at random, what is the probability that they have fewer than $2$ children? Represent this situation with a circle graph.