Frequency Tables

In a high school in Santo Domingo, a study is to be carried out to find out the favorite sport of 1st year of secondary students. Classify the following statistical variables as qualitative or quantitative:

• Favorite sport (Soccer, Basketball, Tennis...).

• Number of hours a week they play sports.

• Brand of sneakers they wear.

• Height in centimeters of each student.

• Number of medals or trophies they have at home.

The leadership team of a school wants to know if the students like the new canteen menu. So as not to ask all 800 students, they have randomly chosen 25 students from each year group to survey them. Identify the following elements of the study:

• Population: _____

• Sample: _____

• Individual: _____

In a secondary school in Santo Domingo, a study is to be carried out on the leisure habits of its students. To do this, the $30$ students of 1st year of secondary C are asked about their favorite social network. Identify, giving reasons, the following elements of the statistical study:

• Population.

• Sample.

• Individual.

• Type of variable (Qualitative or Quantitative).

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

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

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

In a video game shop, they recorded the sales from one morning:

• Action: $12$

• Adventure: $8$

• Sports: $15$

• Strategy: $5$

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

Look at the following frequency table showing the marks on a Mathematics test for $20$ students:

Answer the following questions:

1. How many students achieved a "Good"?

2. Which mark appears most often (the most frequent)?

3. How many students passed the test (considering a pass from "Pass" up to "Excellent")?

A group of friends has recorded the number of times they have been to the cinema in the last six months. The data obtained are:

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

Organise these data into a frequency table including: the value of the variable ($x_i$), the absolute frequency ($f_i$) and the cumulative absolute frequency ($F_i$).

A survey was conducted on the number of pets owned by 20 families. The absolute frequency of families owning "2 pets" is $4$. Calculate the relative frequency ($h_i$) of this value, expressing it as a fraction and as a decimal.

In a 1st year of secondary 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?

A survey was carried out among $40$ teenagers about their favorite sport to play at the municipal sports center. Complete the missing values in the following frequency table, knowing that the sample size is $N = 40$.

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

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

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

In a music class, students were asked how many instruments they can play. The results for 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 can play exactly $2$ instruments?

A streaming platform analysed the number of hours that 40 teenagers spend watching series over 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 these 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.

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

• $H_2$ (Cumulative relative frequency of consuming 2 portions) is $0.75$.

• $f_1 = 12$

• $f_0$ (0 portions) is half of $f_1$.

• The sample total is $N = 40$.

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

For one week, a nutritionist asked $50$ people to record how many portions of fruit they eat a day. The summarised data are:

• $20\%$ eat no fruit.

• $15$ people eat $1$ portion.

• The relative frequency of those who eat $2$ portions is $0.3$.

• The rest eat $3$ portions.

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

In a survey on the number of pets in 50 households in a neighbourhood, the frequency table got smudged and several pieces of data were lost. Your mission is to reconstruct the complete table using the remaining clues:

1. The sample total 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 the number of households with 4 pets.

4. There is only one household with 5 pets.

5. The percentage of households without pets (0) is $12\%$.

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

A 1st-year secondary math test 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 scored 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 scored a 9 is $0.1$.

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

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

From the following bar chart representing the marks obtained by the students of a class in a resit exam, reconstruct the complete frequency table ($x_i, f_i, h_i, \%$).

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

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

• 0 wins: $72^\circ$

• 1 win: $108^\circ$

• 2 wins: $144^\circ$

• 3 wins: 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 wins?

The municipality has recorded the number of occupants in the vehicles that entered the city center yesterday. Errors have been detected in the final report. Identify which data are impossible or incorrect 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.

In a quality control test 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 1 000 h.

• The absolute frequency of those lasting 2 000 h is 30.

• The relative frequency of those lasting 3 000 h is $0.15$.

• The rest of the bulbs lasted 4 000 h.

Organise these data into a frequency table including absolute frequencies, relative frequencies, percentages and cumulative frequencies. What percentage of light bulbs lasted 3 000 hours or more?

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 nobody read more than 4).

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