Frequency tables
You have asked 20 classmates how many times they went to the cinema last month and you have a list of 20 numbers in no particular order. You can't see anything like that. The first step in any study is to sort and count: to make a frequency table.
Frequencies
A group of friends write down the number of times they have been to the cinema in the last month. The data obtained are:…
A group of friends write down the number of times they have been to the cinema in the last month. The data obtained are:
$2, 1, 0, 3, 2, 1, 1, 0, 2, 2, 1, 4, 1, 0, 2, 1, 1, 2, 3, 2$.
Organise these data into a frequency table that includes:
-
The tally (using tally marks).
-
The absolute frequency ($f_i$).
In a 3rd ESO class, students were asked about their favourite sport. Complete the missing values in the following frequency table: | Sport | Absolute frequency ($f_i$) |…
In a 3rd ESO class, students were asked about their favourite sport. Complete the missing values in the following frequency table:
| Sport | Absolute frequency ($f_i$) | Relative frequency ($h_i$) | Percentage (%) |
|---|---|---|---|
| Basketball | $6$ | $0,24$ | $24\%$ |
| Football | $10$ | ||
| Tennis | $4$ | $0,16$ | |
| Swimming | $0,20$ | $20\%$ | |
| Total | $25$ | $1,00$ | $100\%$ |
Fill in the blanks in the following frequency table for a discrete quantitative variable: | Data value ($x_i$) | Abs. frequency ($n_i$) | Rel. frequency ($h_i$) |…
Fill in the blanks in the following frequency table for a discrete quantitative variable:
| Data value ($x_i$) | Abs. frequency ($n_i$) | Rel. frequency ($h_i$) | Percentage frequency ($\%$) |
|---|---|---|---|
| $1$ | $8$ | $0,20$ | |
| $2$ | $0,35$ | ||
| $3$ | $12$ | ||
| $4$ | $15\%$ | ||
| Total | $N=$ | $1,00$ | $100\%$ |
Data grouped into intervals
With continuous variables (or discrete variables with many different values) the data are grouped into intervals or classes, usually of equal width. They are written like this: $[10, 15)$ includes 10 but not 15.
-
Class mark $x_i$: the midpoint of the interval. It represents all the data values in that interval in calculations.
-
Width: the difference between the endpoints.
| Time (min) | Mark $x_i$ | $f_i$ | $F_i$ |
|---|---|---|---|
| $[0, 10)$ | 5 | 3 | 3 |
| $[10, 20)$ | 15 | 8 | 11 |
| $[20, 30)$ | 25 | 6 | 17 |
| $[30, 40)$ | 35 | 3 | 20 |
For a study on the weight of students' backpacks, the data have been grouped into intervals of $1$ kg. Calculate the class mark ($x_i$) for each of the intervals in the…
For a study on the weight of students' backpacks, the data have been grouped into intervals of $1$ kg. Calculate the class mark ($x_i$) for each of the intervals in the table:
| Weight (kg) | Class mark ($x_i$) | Frequency ($f_i$) |
|---|---|---|
| $[2, 3)$ | $4$ | |
| $[3, 4)$ | $12$ | |
| $[4, 5)$ | $9$ | |
| $[5, 6)$ | $5$ |
A courier company studies the weight of the parcels it sends daily. It has organised the information in the following table of cumulative relative frequencies ($H_i$): |…
A courier company studies the weight of the parcels it sends daily. It has organised the information in the following table of cumulative relative frequencies ($H_i$):
| Weight (kg) | $f_i$ | $h_i$ | $H_i$ |
|---|---|---|---|
| $[0, 2)$ | $20$ | $0,40$ | $0,40$ |
| $[2, 4)$ | $15$ | $0,30$ | $0,70$ |
| $[4, 6)$ | $10$ | $0,20$ | $0,90$ |
| $[6, 8)$ | $5$ | $0,10$ | $1,00$ |
Answer the following questions based on the table:
- a) What percentage of packages weigh less than $4$ kg?
- b) What relative frequency is represented by packages weighing $6$ kg or more?
- c) What is the total number of packages analysed in this study?
The time, in minutes, taken by $20$ students to get from home to school has been measured. The data are:…
The time, in minutes, taken by $20$ students to get from home to school has been measured. The data are:
$5, 12, 18, 24, 7, 15, 30, 10, 22, 14, 8, 11, 28, 5, 19, 13, 16, 25, 12, 9$
Construct a frequency table by grouping the data into $5$ intervals of equal width, starting at $5$ and ending at $30$. Include in the table the class marks ($x_i$) and the absolute frequencies ($n_i$).
You can do it on paper and send a photo with your answer.