Frequency tables
You have asked 20 classmates how many pets they have and you have ended up with 20 jumbled numbers. It makes no sense like that. The first step in any statistical study is to sort and count: to make a frequency table.
Absolute and relative frequency
In a secondary school in Madrid, a study is to be carried out to find out the favourite sport of 1st ESO students. Classify the following statistical variables as…
In a secondary school in Madrid, a study is to be carried out to find out the favourite sport of 1st ESO students. Classify the following statistical variables as qualitative or quantitative:
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Favourite sport (Football, Basketball, Tennis...).
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Number of hours a week they do sport.
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Brand of trainers they wear.
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Height in centimetres of each student.
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Number of medals or trophies they have at home.
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…
In a video game shop, they recorded the sales from one morning:
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Action: $12$
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Adventure: $8$
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Sports: $15$
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Strategy: $5$
Calculate the value of $N$ (the total number of data values) by adding the absolute frequencies of all the categories.
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:…
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 ($F_i$).
Your first investigation with a spreadsheet
Question: how many books did each student in our class finish reading last month? Agree on what "finishing a book" means and ask the whole class, with no names in the results table. Also record how many people do not answer: they are not zeros. Do not ask only those who go to the library, because that could bias the answer.
To learn the procedure we will use eight made-up answers: 0, 1, 1, 2, 2, 2, 3, 5. They are not real data from the class.
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In A1 type
Libros; in A2:A9, the eight values, one per cell. -
In C1 type
Librosand in D1,Frecuencia. Fill C2:C7 with 0, 1, 2, 3, 4, 5. -
In D2 type
=CONTAR.SI($A$2:$A$9;C2)and copy down to D7. You should get 1, 2, 3, 1, 0, 1. The references with$keep the range of answers fixed when you copy. -
In E1 type
Frecuencia relativa. In E2 type=D2/CONTAR($A$2:$A$9)and copy down to E7. Apply percentage format if you need to. -
Check
=SUMA(D2:D7): it should give 8. With=SUMA(E2:E7)you should get 1, or 100 % if you display it as a percentage. -
Select C1:D7 and insert a column chart with separate columns: "Libros" on the horizontal axis and "Estudiantes" on the vertical axis, starting at zero. Give it a title that states the group and the period studied.
Applications may use other names or separators depending on their language; look for the functions that count with a condition, count numbers and add up.
Sharing the work and checking for mistakes
In pairs, one person enters the data and the other checks the counts; swap roles when you create the chart. Before accepting a conclusion, each of you explains why the data support it. If you disagree, compare specific rows instead of deciding who is "better at maths". Do not share out tasks by gender or by supposed ability: everyone should practise and be listened to.
If you get stuck, identify what is worrying you and make the task smaller: first try it with three answers and count them by hand. Finish by writing "My mistake was…; I found it when…; next time I will check…". Asking for help and changing strategy is also learning.
Cumulative frequency
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…
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.
A recycling centre analysed the contents of a recycling bin for plastics and cans. $45\%$ of the items were plastic bottles, $30\%$ were soft drink cans, $15\%$ were…
A recycling centre analysed 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 analysed, construct a frequency table showing the absolute frequency of each type of waste.
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 pie chart representing these data has the following angles for…
In an e-sports tournament, the number of victories of 80 participants is recorded. It is known that the pie chart representing these data has the following angles for each category:
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0 wins: $72^\circ$
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1 win: $108^\circ$
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2 wins: $144^\circ$
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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?
You can do it on paper and send a photo with your answer.