Frequency tables
You have asked 20 classmates how many pets they have, and you have 20 jumbled numbers in your notebook. Like this, it makes no sense: the first step is to sort and count, that is, to build a frequency table.
Absolute, relative and cumulative frequency
A study is to be carried out to find out the favorite book of the $1\,200$ students of a secondary school in Madrid. To do so, $80$ students are chosen at random and…
A study is to be carried out to find out the favorite book of the $1\,200$ students of a secondary school in Madrid. To do so, $80$ students are chosen at random and asked the title of the book they have liked the most this year.
Identify the following elements of this statistical study:
-
Population
-
Sample
-
Individual
The following table shows the number of pets that the families in a housing development have. Complete the column of cumulative absolute frequencies ($N_i$): | Nº of…
The following table shows the number of pets that the families in a housing development have. Complete the column of cumulative absolute frequencies ($N_i$):
| Nº of pets ($x_i$) | Absolute frequency ($n_i$) | Cumulative frequency ($N_i$) |
|---|---|---|
| $0$ | $8$ | |
| $1$ | $12$ | |
| $2$ | $7$ | |
| $3$ | $3$ | |
| Total | $30$ | --- |
Hint. The cumulative frequency of each row is the sum of its absolute frequency and the cumulative frequency of the previous row. The first row carries over directly: $N_1 = n_1$. The last cumulative frequency must match the total.
In a survey on the number of pets owned by families in a Year 9 class, the following incomplete table was produced. Complete it in your exercise book knowing that the…
In a survey on the number of pets owned by families in a Year 9 class, the following incomplete table was produced. Complete it in your exercise book knowing that the total number of students is $30$.
| Pets ($x_i$) | Abs. frequency ($n_i$) | Cum. absolute frequency ($N_i$) | Cum. relative frequency ($H_i$) |
|---|---|---|---|
| 0 | 12 | ||
| 1 | 9 | ||
| 2 | 26 | ||
| 3 | 4 |
What percentage of students have at most one pet?
Data grouped into intervals
When the variable is continuous (time, height…) with many different values, the data are grouped into intervals of the form $[a, b)$ (includes $a$, does not include $b$).
A study has been carried out on the distance (in km) that $40$ people travel to get to their workplace. The data have been grouped into the following intervals:…
A study has been carried out on the distance (in km) that $40$ people travel to get to their workplace. The data have been grouped into the following intervals: $[0, 4)$, $[4, 8)$, $[8, 12)$ and $[12, 16)$.
Given that the absolute frequencies are $14$, $10$, $8$ and $8$ respectively:
- a) Construct the frequency table including the class mark ($c_i$) of each interval.
- b) How many people travel $8$ km or more?
You can do it on paper and send a photo with your answer.
Students in a class were asked how many hours on average they spend studying per day. Some data in the table have been lost. Complete it knowing that the total number of…
Students in a class were asked how many hours on average they spend studying per day. Some data in the table have been lost. Complete it knowing that the total number of students is $25$.
| Hours of study ($x_i$) | Frequency ($n_i$) | Relative frequency ($f_i$) |
|---|---|---|
| $1$ h | $5$ | $0,20$ |
| $2$ h | $0,40$ | |
| $3$ h | $6$ | |
| $4$ h | $4$ | $0,16$ |
| Total | $25$ | $1$ |
Two-way tables
When two variables are cross-tabulated at the same time (for example, preferred music and sex), a two-way table is used: the rows are the values of one variable and the columns those of the other.
A survey was carried out among secondary school students about their favourite sport. The results are shown in this two-way table, but some data are missing. Complete…
A survey was carried out among secondary school students about their favourite sport. The results are shown in this two-way table, but some data are missing. Complete it.
| Football | Basketball | Tennis | TOTAL | |
|---|---|---|---|---|
| Girls | $45$ | $20$ | $95$ | |
| Boys | $25$ | $15$ | ||
| TOTAL | $105$ | $55$ |
Using the table, calculate the percentage of (total) students who prefer basketball.
A survey on the use of three streaming platforms (A, B, and C) was conducted among 2nd year ESO students. This incomplete two-way table relates the preferred platform to…
A survey on the use of three streaming platforms (A, B, and C) was conducted among 2nd year ESO students. This incomplete two-way table relates the preferred platform to the primary device used.
| Tablet | Smartphone | PC | TOTAL | |
|---|---|---|---|---|
| Platform A | $8$ | $5$ | ||
| Platform B | $14$ | $22$ | ||
| Platform C | $6$ | $7$ | $25$ | |
| TOTAL | $18$ | $35$ |
Knowing that the total number of surveyed students is $69$, complete the table and calculate what percentage of the total students mainly uses a Smartphone to watch Platform B.