7.02 Frequency and mode
A gymnast received the following scores over 12 rounds of a competition:
Find the missing frequency to find how many times the gymnast scored 8.
| Score | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|
| Frequency | 2 | 1 | 1 | 1 |
Bill asks nine of his friends which pet they would like and writes down their responses:
\text{Dog, Fish, Cat, Cat, Fish, Dog, Fish, Fish, Dog}Construct a frequency table for these responses.
A school nurse is investigating the number of sick days taken by students in a class, and constructs the following table:
Construct a frequency table for the number of sick days.
State the number of students who had no sick days.
State the most common number of sick days for the class.
| Student | Sick days |
|---|---|
| \text{Sally} | 0 |
| \text{Lachlan} | 2 |
| \text{Tara} | 1 |
| \text{Xavier} | 4 |
| \text{Luigi} | 2 |
| \text{Nadia} | 4 |
| \text{Lisa} | 0 |
| \text{Dave} | 1 |
| \text{Bill} | 3 |
| \text{Danielle} | 4 |
Brad stands at the school gate and tallies the hair color of students as they enter the school. His results are shown in the table:
Construct a frequency table from Brad's tally.
Find the total number of students Brad tallied.
What fraction of students had red hair?
The following table shows the number of trains arriving either on time or late, at Central station during one week:
How many trains arrived on time on Thursday?
How many trains arrived late on Wednesday?
What fraction of the total trains arriving during the week, arrived on Friday?
What fraction of the trains arriving on Sunday were on time?
| Day | Trains on time | Trains arriving late |
|---|---|---|
| \text{Monday} | 14 | 6 |
| \text{Tuesday} | 16 | 4 |
| \text{Wednesday} | 18 | 2 |
| \text{Thursday} | 15 | 5 |
| \text{Friday} | 17 | 3 |
| \text{Saturday} | 6 | 6 |
| \text{Sunday} | 5 | 3 |
Find the mode(s) of the following sets of scores:
12, 12, 13, 11, 13, 9, 13, 14, 9
14, 2, 5, 2, 2, 5, 5, 7, 12, 13, 13, 14
| Score | 21 | 22 | 23 | 24 | 25 | 26 |
|---|---|---|---|---|---|---|
| Frequency | 31 | 37 | 39 | 33 | 38 | 34 |
Thomas conducted a survey on the average number of hours his classmates exercised per day and displayed the data in the table.
How many classmates did Thomas survey?
What is the mode of the data?
How many classmates exercised for less than three hours?
How many classmates exercised for at least three hours?
| No. exercise hours | Frequency |
|---|---|
| 0 | 2 |
| 1 | 12 |
| 2 | 7 |
| 3 | 5 |
| 4 | 0 |
| 5 | 3 |
Mrs. Tran asks her students how many bedrooms they have in their house and writes their responses below:
3, 3, 4, 4, 3, 3, 4, 5, 2, 2, 4, 4
Complete the frequency table.
How many students did Mrs Tran survey?
State the modal number of bedrooms.
| Number of Bedrooms | Number of Students |
|---|---|
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 |
Ms. Lee bought pizza for her class. She told her students they could eat as much as they wanted in two minutes. She counted up how many slices each student ate in that time and wrote her results below:
2, \, 2, \, 2, \, 3, \, 6, \, 0, \, 2, \, 3, \, 4, \, 2, \, 1, \, 1, \, 2, \, 2, \, 6
Complete the frequency table for this data.
How many students are in the class?
State the modal number of slices eaten.
| Slices eaten | Number of Students |
|---|---|
| 0 | |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 |
Yvonne asks a number of her friends what their favorite color is, and writes down their reponses below:
\text{Blue, Pink, Blue, Yellow, Green, Pink, Pink, Yellow,}\\ \text{ Green, Blue, Yellow, Pink, Yellow, Pink, Pink}
Construct a frequency table.
How many friends did Yvonne survey?
Which color is the mode?
The frequency table shows the resting heart rates of a number of people taking part in a study:
Find the number of people taking part in the study.
How many people had a resting heart rate between 40 and 59 beats/minute?
How many people had a resting heart rate of below 50 beats/minute?
| Heart Rate | Frequency |
|---|---|
| 30 - 39 | 20 |
| 40 - 49 | 22 |
| 50 - 59 | 28 |
| 60 - 69 | 37 |
A group of 30 people was surveyed about how many video games they had played in the past month. The results are shown in the given table:
Find the number of people who played 10 or more video games.
Find the number of people who played less than 5 games.
Find the number of people who played more than 4, but less than 15 video games.
State the modal class for the data.
| \text{Number of video } \\\ \text{games played} | \text{Frequency} |
|---|---|
| 0 - 4 | 5 |
| 5 - 9 | 12 |
| 10 - 14 | 9 |
| 15 - 19 | 4 |
Neil tracks how many views his website receives each week for ten weeks. The results are given in the following table:
| Week | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| Views | 601 | 612 | 618 | 620 | 636 | 643 | 644 | 659 | 670 | 691 |
Construct a frequency table for this data set by grouping the data into sets of twenty, with the first group being 600-619.
Consider the data below:
48, \, 31, \, 85, \, 46, \, 56, \, 33, \, 66, \, 48, \, 86, \, 74, \, 64, \, 63, \, 50, \\\\ 52, \, 62, \, 67, \, 33, \, 66, \, 81, \, 40, \, 58, \, 63, \, 68, \, 58, \, 78
Construct a frequency table for this data by grouping the data into sets of ten, with the first group being 30-39.
Fifteen airline passengers weigh their luggage. The weights in kilograms are listed below:
17, 20, 19, 19, 20, 21, 20, 22, 20, 19, 17, 16, 20, 20, 16
Construct a frequency table for this data.
How many passengers had luggage that weighed more than 20 kilograms?
The airline charges each passenger \$3 for every kilogram above 20 kilograms. Calculate the total charge for overweight luggage for this group of passengers.
A PE teacher asked her students to do as many push-ups as they could, and recorded the number of push-ups each student completed below:
38, \, 31, \, 12, \, 14, \, 29, \, 7, \, 21, \, 19, \, 46, \, 13, \, 23, \, 3, \, 13, \, 17, \, 4, \, 6, \, 11, \, 24, \, 5, \, 20
Construct a frequency table for this data set by grouping data into sets of ten, with the first group being 0-9.
Find the number of students in the class.
How many students could perform at least 30 pushups?
How many students could not perform at least 40 pushups?