Exercises: Data representation

A survey has been carried out in a 7th grade class to find out which social network is preferred by the students. The following results have been obtained: Instagram, TikTok, TikTok, YouTube, Instagram, TikTok, YouTube, Instagram, Instagram, TikTok, YouTube, TikTok, Instagram, YouTube, Instagram.

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

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

From the graph, answer:

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

The students in a class were asked about 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 that includes the absolute frequency ($n_i$) and the relative frequency ($f_i$).

To represent the results of a survey on favorite ice cream flavor in a pie chart, we need to calculate the angles of each section. If we know that $10$ people out of a total of $40$ like chocolate, what angle in degrees ($^\circ$) will the circular 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 questions:

1. a) How many trees were planted in 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) it takes $25$ students to get to school from their home has been recorded. The data has been grouped in the following interval table:

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

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 know how many hours a week young people aged $12$ to $14$ play. They have asked $100$ boys and girls chosen at random from different middle schools in the US.

State in this case:

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 the use of social networks, $40$ teenagers at a middle school were asked what their favorite platform is. The results obtained are as follows:

• TikTok: $18$ people.

• Instagram: $12$ people.

• YouTube: $6$ people.

• BeReal: $4$ people.

1. a) Identify the population, the sample and the type of statistical variable.
2. b) Create a frequency table that includes the absolute frequency ($n_i$), the relative frequency ($f_i$) and the percentage ($\%$) for each value.
3. c) Represent the data in a bar chart.

The number of books read by the students in a 7th grade class during the first quarter has been recorded. The data is:

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

1. a) Create the table of absolute and cumulative absolute frequencies ($N_i$).
2. b) What percentage of students have read $2$ books or fewer?
3. c) Represent a frequency polygon on the absolute frequency bar chart.

A video game company wants to represent the type of console preferred by users at a gaming fair in a pie chart. The data is:

• PlayStation: $45\%$

• Nintendo Switch: $30\%$

• Xbox: $15\%$

• PC: $10\%$

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

The height (in inches) of the $20$ members of a youth basketball club has been measured. As it is a continuous variable, the data has been grouped into the following intervals:

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

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

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

The town council of a city wants to raise awareness about recycling. To do this, it has published a pictogram on 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 absolute 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 this same data using a bar chart to compare both methods of visualization.

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

1. a) Explain why Graph B gives a feeling of much faster growth than Graph A if the data is identical.
2. b) Which of the two graphs seems more objective to you for informing the public? Justify your answer based on the scale of the y-axis.

A climate graph is a graph that combines a bar chart (rainfall) and a line graph (temperatures). Look at the simplified data for a quarter in a city in Southern California:

• 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, the rainfall on the left $Y$ axis (bars) and the temperatures on the right $Y$ axis (line).
2. b) Analyzing the graph, what trend do you observe in the transition from winter to spring?

A survey has been carried out 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 pie chart.
3. c) State what the mode of this study is.

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

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

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

1. a) What is the median battery life 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 quartiles.
3. c) Which of the two models has a more dispersed distribution in the central $50\%$ of the data?

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

1. a) Explain why the graph for Social Network Y might be misleading for their sponsors if they do not look at the y-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 a suitable scale that allows the real growth of both accounts to be compared.

The town council of a city has collected data on the recycling of domestic organic waste from $200$ families. The following pie chart shows the distribution, but the data for the families who recycle "A lot" has been erased.

• Nothing ($0$ pounds/month): $15\%$

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

• Average ($6-10$ pounds/month): $90$ families

• A lot ($>10$ pounds/month): $?$

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

In a study on the use of the school library, the number of books borrowed by a sample of 7th grade students during a quarter has been 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 absolute frequency table ($n_i$) from the cumulative frequencies.
3. c) What is the mode and the median of the number of books borrowed?
4. d) Represent the data using a pie chart.

A survey has been carried out among $400$ teenagers about their favorite weekend activity, differentiating between boys and girls. The data is collected 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 chart (one bar for boys and another for girls for each activity).
3. c) What percentage of the 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 has been 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 event knowing that in the interval $[0,15, 0,20)$ there were $12$ athletes.
2. b) Calculate the midpoint of each interval.
3. c) Estimate the arithmetic mean of the reaction times from the data in the histogram.
4. d) What percentage of athletes have a reaction time of less than $0,20$ seconds?

An NGO has carried out 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 this amount in 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 pie chart.