Frequency Tables

The management of a school wants to know if the students like the new cafeteria menu. To avoid asking all 800 students, they have randomly chosen 25 students from each grade level to survey them. Identify the following elements of the study:

• Population: _____

• Sample: _____

• Individual: _____

A middle school in Chicago wants to carry out a study on the leisure habits of its students. To do this, the $30$ students of 6th Grade C are asked about their favorite social network. Identify with reasoning the following elements of the statistical study:

• Population.

• Sample.

• Individual.

• Type of variable (Qualitative or Quantitative).

In a middle school in Dallas, a study is to be carried out to find out the favorite sport of 6th grade students. Classify the following statistical variables as qualitative or quantitative:

• The preferred sport (Soccer, Basketball, Tennis...).

• The number of hours a week they practice sport.

• The brand of sneakers they wear.

• The height in inches of each student.

• The number of medals or trophies they have at home.

During recess, we asked a group of friends what their favorite fruit for a snack is. The results were:

Apple, Banana, Pear, Apple, Apple, Pear, Banana, Apple, Pear, Banana.

Create a frequency table in your notebook that includes a column for the Tally (using tally marks) and another for the Absolute Frequency ($f_i$).

In a video game store they have noted down the sales of a morning:

• Action: $12$

• Adventure: $8$

• Sports: $15$

• Strategy: $5$

Calculate the value of $N$ (the total number of data) by adding the absolute frequencies of all the categories.

Look at the following frequency table showing the Math exam grades of $20$ students:

Answer the following questions:

1. How many students got a "Good"?

2. What is the most repeated grade (the most frequent)?

3. How many students passed the exam (considering a pass is from Pass to Excellent)?

A survey has been carried out on the number of pets that 20 families have. The absolute frequency of families that have "2 pets" is $4$. Calculate the relative frequency ($h_i$) of this value, expressing it as a fraction and as a decimal.

In a 6th grade class, $20\%$ of the students walk to school. If the relative frequency in the table is $0,25$ for those who come by bus, what percentage of students does this last figure represent?

Copy and complete the missing data in this frequency table about the eye color of a group of people. Remember that the sum of the relative frequencies must be $1$.

A group of friends has noted down the number of times they have been to the movie theater in the last six months. The data obtained are:

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

Organize this data into a frequency table that includes: the value of the variable ($x_i$), the absolute frequency ($f_i$) and the cumulative absolute frequency ($F_i$).

In a music class, the students have been asked how many instruments they know how to play. The results of the cumulative absolute frequency ($F_i$) are:

• $0$ instruments: $F_1 = 4$

• $1$ instrument: $F_2 = 15$

• $2$ instruments: $F_3 = 22$

• $3$ instruments: $F_4 = 25$

Calculate the absolute frequency ($f_i$) for each value and determine how many students there are in total in the class. What percentage of students knows how to play exactly $2$ instruments?

A streaming platform has analyzed the number of hours that 40 teenagers spend watching shows during the weekend. They have only provided us with the Cumulative Absolute Frequencies column ($F_i$):

• 1 hour: $F_1 = 6$

• 2 hours: $F_2 = 15$

• 3 hours: $h_3 = 0,25$ (Relative frequency, not cumulative)

• 4 hours: $F_4 = 34$

• 5 hours: $F_5 = 40$

From this data, obtain the complete frequency table, including the Absolute Frequency ($f_i$) of each value, the Cumulative Relative Frequency ($H_i$), and the Percentage ($\%$) of each one.

A survey has been carried out on $40$ teenagers about their preferred sport to practice at the community sports center. Complete the missing values in the following frequency table knowing that the sample size is $N = 40$.

A recycling center has analyzed the contents of a recycling bin. $45\%$ of the objects were plastic bottles, $30\%$ were soda cans, $15\%$ were milk cartons and the rest were other metal containers. If a total of $200$ objects were analyzed, construct a frequency table showing the absolute frequency of each type of waste.

Over a week, a nutritionist has asked $50$ people to note down how many pieces of fruit they eat a day. The summarized data are:

• $20\%$ eat no pieces.

• $15$ people eat $1$ piece.

• The relative frequency of those who eat $2$ pieces is $0,3$.

• The rest eat $3$ pieces.

Construct the complete frequency table and answer: What number or numbers of pieces of fruit are the mode of this study?

In a survey on the number of pets in 50 households in a neighborhood, the frequency table has been stained and several pieces of data have been lost. Your mission is to reconstruct the complete table using the remaining clues:

1. The total of the sample is $N = 50$.

2. The relative frequency of having 1 pet is exactly $0,32$.

3. The number of households with 3 pets is double that of households with 4 pets.

4. There is only one household with 5 pets.

5. The percentage of households with no pets (0) is $12\%$.

Complete the table by calculating the Absolute Frequency ($f_i$), Relative Frequency ($h_i$), and the Percentage ($\%$) for each value.

A 6th grade math exam has grades from 1 to 10. The teacher gives us the following information about the results of the 30 students:

1. $20\%$ of the class got a 5.

2. The grades 1, 2, 3, and 10 have an absolute frequency of 0.

3. There is the same number of students with a 6 as with a 7.

4. The relative frequency of those who got a 9 is $0,1$.

5. There are 4 students with a 4 and 3 students with an 8.

Find how many students got a 6 and a 7, and create the complete frequency table with all the studied columns ($f_i, F_i, h_i, H_i, \%$).

In a quality control at a light bulb factory, 120 units are tested to see how many hours they last before failing (rounded to thousands of hours). The collected data are:

• $35\%$ lasted 1,000h.

• The absolute frequency of the 2,000h ones is 30.

• The relative frequency of the 3,000h ones is $0,15$.

• The rest of the light bulbs lasted 4,000h.

Organize this data into a frequency table that includes absolute frequencies, relative frequencies, percentages and cumulative frequencies. What percentage of light bulbs lasted 3,000 hours or more?

A study has been carried out on the daily fruit consumption in a sample of people. We know that:

• $H_2$ (Cumulative relative frequency of consuming 2 pieces) is $0,75$.

• $f_1 = 12$

• $f_0$ (0 pieces) is half of $f_1$.

• The total of the sample is $N = 40$.

Calculate the absolute frequency of consuming 2 pieces ($f_2$) and complete the table for the values 0, 1, 2, and 3 (knowing that 3 is the maximum value of the study).

A group of students is asked about the number of books read in the last year. We are not given the total number of students, but we know that:

• Absolute frequency of 1 book: $f_1 = 8$.

• Relative frequency of 1 book: $h_1 = 0,16$.

• Cumulative relative frequency up to 2 books: $H_2 = 0,5$.

• Absolute frequency of 3 books: $f_3 = 15$.

• The rest of the students read 4 books (every student read at least 1 book and no one read more than 4).

First, calculate the population size ($N$). Then, complete the frequency table and find out how many students read 4 books.

A study has been carried out on the number of siblings of the students at a school. The researcher has made some errors when calculating the relative frequencies. State what they are and correct them so that the table is valid.

Hint: Check the total sum of the relative frequencies.

The city council has recorded the number of occupants of the vehicles that entered the city center yesterday. Errors have been detected in the final report. Identify which data are impossible or erroneous in the following table of 200 vehicles and correct it assuming that, in the "3 people" row, the incorrect value is the one in column $f_i$ (not those of $h_i$ or the percentage):

Hint: Look at the sum of the frequencies and the consistency between columns.

From the following bar chart representing the grades obtained by the students of a course on a retake exam, reconstruct the complete frequency table ($x_i, f_i, h_i, \%$).

In an e-sports tournament, the number of victories of 80 participants is recorded. It is known that the pie chart representing this data has the following angles for each category:

• 0 victories: $72^\circ$

• 1 victory: $108^\circ$

• 2 victories: $144^\circ$

• 3 victories: The rest of the circle.

Construct the complete frequency table ($f_i$, $h_i$, $\%$) knowing that the total number of individuals is $N = 80$. How many players achieved the maximum number of victories?