The frequency of a value in a data set is the number of times that the value appears in the data set.
For example, consider the following data set, which shows the time that some students in a class spent studying for a final exam:
We compute the frequency of the values in our data set as follows:
the frequency of is because the value appears times in the data set
the frequency of is because the value appears times in the data set
Likewise:
the frequency of is
the frequency of is
the frequency of is
To represent this data set concisely, we can use a frequency table like the one shown below:
| Hours Studied | Frequency |
|---|---|
Heather surveyed the amount of milk consumed per week by several households. The results are shown in the following frequency table.
| Liters of Milk | Frequency |
|---|---|
How many respondents said they consumed liters of milk per week?
First, let's highlight the relevant row in the table.
| Liters of Milk | Frequency |
|---|---|
From the table, we can see that households consume liters of milk per week.
A teacher graded the results of a math test using a $4$-point scale. The distribution of the grades is shown in the following frequency table.
| Grade | Frequency |
|---|---|
| $1$ | $3$ |
| $2$ | $6$ |
| $3$ | $8$ |
| $4$ | $5$ |
How many students got a grade of $3$ on the test?
|
a
|
$5$ students |
|
b
|
$1$ student |
|
c
|
$6$ students |
|
d
|
$2$ students |
|
e
|
$8$ students |
Several people were interviewed about the number of portable electronic devices they owned. The following frequency table shows the distribution of the responses obtained.
| Number of E-devices | Frequency |
|---|---|
| $0$ | $2$ |
| $1$ | $10$ |
| $2$ | $15$ |
| $3$ | $12$ |
How many people responded that they have only one electronic device?
|
a
|
$12$ people |
|
b
|
$7$ people |
|
c
|
$15$ people |
|
d
|
$20$ people |
|
e
|
$10$ people |
Sometimes, we may wish to consider putting data set values into groups before writing down a frequency table.
Let's again consider the following frequency table, showing the time some students spent studying for the final exam:
| Hours Studied | Frequency |
|---|---|
Suppose we wish to compare the number of students who studied for hours to those who studied for hours. We start by writing down the frequency of each group:
Looking at the top three rows in the table, we see that students studied for hours.
Looking at the bottom two rows in the table, we see that students studied for hours.
We can present our results using a grouped frequency table, as follows:
| Hours Studied | Frequency |
|---|---|
There are advantages and disadvantages to grouped frequency tables:
Smaller tables are generally easier to work with, so grouped tables are helpful when dealing with large amounts of data.
However, we lose information when using a group frequency table. For example, it's impossible to determine how many students studied for exactly hours using only this table.
Mike, a sales consultant, recorded the number of smartphones sold by a store each hour over a certain period. The results are given below:
What is the missing number in the frequency table below representing the same data?
| Number of Smartphones | Frequency |
|---|---|
We need to count the number of smartphones for the group
From the data, there were hours when the number of smartphones sold was between and :
Therefore, the missing value is
| Number of Smartphones | Frequency |
|---|---|
Samuel counted the number of phone calls that his company received each day over the past week. The results are given below:
\[ 55, \: 24, \: 29, \: 31, \: 45, \: 12, \: 5 \]
What is the missing number in the frequency table below?
| Number of Calls | Frequency |
|---|---|
| $1-20$ | $2$ |
| $21-40$ | $\fbox{$\,\phantom{0}\,$}$ |
| $41-60$ | $2$ |
|
a
|
$7$ |
|
b
|
$4$ |
|
c
|
$3$ |
|
d
|
$1$ |
|
e
|
$2$ |
Margaret, a marketing advisor, counted the number of cakes sold by a bakery each Friday over a certain period. The results are given below:
\[ 13, \: 4, \: 15, \: 3, \: 12, \: 7, \: 17 \]
From top to bottom, what are the missing numbers in the frequency table below?
| Number of Cakes | Frequency |
|---|---|
| $1-5$ | $2$ |
| $6-10$ | $\fbox{$\,\phantom{0}\,$}$ |
| $11-15$ | $\fbox{$\,\phantom{0}\,$}$ |
| $16-20$ | $1$ |
|
a
|
$2$ and $3$ |
|
b
|
$3$ and $2$ |
|
c
|
$1$ and $2$ |
|
d
|
$1$ and $3$ |
|
e
|
$3$ and $1$ |
Mary asked some family members how many glasses of water they drink daily. The results are shown in the following frequency table.
| Glasses of Water | Frequency |
|---|---|
How many family members did Mary consult?
From the frequency table:
of Mary's family members drink between and glasses per day
of Mary's family members drink between and glasses per day
of Mary's family members drink between and glasses per day
of Mary's family members drink between and glasses per day
To find out the total number of family members that Mary consulted, we add up the frequencies:
So, Mary consulted a total of members of her family.
The teacher asked all students in her class how many different US states they had visited in the past three years. The results are given in the following frequency table. How many students are in her class?
| Number of States Visited | Frequency |
|---|---|
| $1-3$ | $9$ |
| $4-6$ | $6$ |
| $7-9$ | $3$ |
| $10-12$ | $2$ |
|
a
|
$25$ |
|
b
|
$15$ |
|
c
|
$20$ |
|
d
|
$22$ |
|
e
|
$12$ |
The following frequency table shows the distribution of the number of points scored by every player of a basketball team in their last game. How many players from the team played in the last game?
| Number of Points Scored | Frequency |
|---|---|
| $1-6$ | $4$ |
| $7-12$ | $7$ |
| $13-18$ | $3$ |
| $19-24$ | $1$ |
|
a
|
$24$ |
|
b
|
$16$ |
|
c
|
$15$ |
|
d
|
$18$ |
|
e
|
$12$ |
The following frequency table shows the number of home runs scored by the players of a baseball team during some playoffs. How many players batted between and home runs?
| Home Runs | Frequency |
|---|---|
| Home Runs | Frequency |
|---|---|
From the frequency table:
players batted between home runs
players batted between home runs
Therefore, players batted between and home runs.
The following frequency table shows the number of apps, grouped by price, sold by a computer programmer over a certain period. How many apps were sold for at least $\$150?$
| Price ($\$$) | Number of Apps |
|---|---|
| $50-99$ | $14$ |
| $100-149$ | $9$ |
| $150-199$ | $13$ |
| $200-249$ | $10$ |
|
a
|
$21$ |
|
b
|
$13$ |
|
c
|
$10$ |
|
d
|
$18$ |
|
e
|
$23$ |
The following frequency table shows the charge percentage of a series of car batteries in a motor garage. How many batteries have a charge of either $40\%$ or $50\%?$
| Charge ($\%$) | Frequency |
|---|---|
| $20$ | $4$ |
| $30$ | $3$ |
| $40$ | $8$ |
| $50$ | $9$ |
| $60$ | $6$ |
|
a
|
$23$ |
|
b
|
$9$ |
|
c
|
$17$ |
|
d
|
$8$ |
|
e
|
$13$ |