Construct a frequency table for the data in the given stem and leaf plot:
| Leaf | |
|---|---|
| 1 | 1\ 2\ 3\ 7 |
| 2 | 3\ 4\ 7\ 7\ 7\ 9 |
| 3 | 2\ 7\ 9 |
| 4 | 0\ 1\ 1\ 5\ 6 |
| 5 | 2\ 6 |
Key: 1 \vert 2 = 12
For the following surveys, state whether the data found should be grouped or ungrouped when constructing a frequency table:
A survey conducted of 1000 people, asking them how many languages they speak.
A survey conducted of 1000 people, asking them how many different countries they know the names of.
Some data is grouped into class intervals. One of the class intervals is 5-9, find the upper bound of another class interval with 25 as a lower bound.
The following frequency table shows the data distribution for the length of leaves collected from a species of tree in the botanical gardens:
How many leaves less than 60 \text{ mm} were collected?
What was the most common interval of leaf length collected?
Are leaves more likely to be at least 60 \text{ mm} in length?
Can we conclude from the table that there were no leaves collected with a length less than 5 \text{ mm}. Explain your answer.
| Leaf length, (mm) | Frequency |
|---|---|
| 0 \leq x \lt 20 | 5 |
| 20\leq x \lt 40 | 11 |
| 40\leq x \lt 60 | 19 |
| 60\leq x \lt 80 | 49 |
| 80\leq x \lt 84 | 43 |
The following frequency table below shows the resting heart rate of some people taking part in a study:
Complete the table.
How many people took part in the study?
How many people had a resting heart rate from 55 to 74?
How many people had a resting heart rate of below 65?
| Heart Rate | Class Centre | Frequency |
|---|---|---|
| 45-54 | 15 | |
| 55-64 | 25 | |
| 65-74 | 26 | |
| 75-84 | 30 |
As part of a fuel watch initiative, the price of petrol at a service station was recorded each day for 20 days. The frequency table shows the findings:
What was the highest price that could have been recorded?
What is the modal price range?
What percentage of instances was the petrol price in the modal price range?
If the class centres are taken to be the score in each class interval, find the total of the prices recorded.
Hence, find the average fuel price.
| Price (in cents per litre) | Frequency |
|---|---|
| 130.0-134.9 | 5 |
| 135.0-139.9 | 6 |
| 140.0-144.9 | 3 |
| 145.0-149.9 | 4 |
| 150.0-154.9 | 2 |
The same machinery is produced at two different plants. The number of faults detected in the machinery is recorded each day for several days, and the results are in the graph below:
State the class intervals, given that the lowest score is 0 and the highest is 19.
On how many days were less than 10 faults detected at Plant A?
Using the class centres, what was the total number of faults at Plant A?
Using the class centres, what are the total number of faults detected at Plant B?
Construct a grouped frequency table for the following data:
46,\, 54,\, 35,\, 23,\, 24,\, 28,\, 26,\, 11,\, 19,\, 17,\, 32
83,\, 68,\, 39,\, 42,\, 86,\, 66,\, 64,\, 76,\, 63,\, 43,\, 65,\, 83,\, 63,\, 67,\, 49,\, 51,\, 32,\, 55,\, 38,\, 65,\, 41,\, 73,\, 35,\, 36,\, 74
Use the given histogram to construct a frequency table:
Lachlan wanted to see whether his car’s fuel consumption is the same as the fuel consumption stated by the car company. He measured his fuel consumption (in litres) over several journeys of equal distance:
9.1, \quad 9.1, \quad 9.1, \quad 9.1, \quad 9.2, \quad 9.2, \quad 9.3, \quad 9.4, \quad 9.5, \quad 9.5,\\ 9.6, \quad 9.7, \quad 9.7, \quad 9.8, \quad 9.8, \quad 9.8,\quad 9.8, \quad 9.9, \quad 10.1, \quad 10.1,\\ 10.1, \quad 10.1, \quad 10.2, \quad 10.2, \quad 10.2, \quad 10.2, \quad 10.2, \quad 10.2,\quad 10.3,\quad 10.4,\\10.4, \quad 10.5, \quad 10.6, \quad 10.6, \quad 10.7, \quad 10.8, \quad 10.9, \quad 10.9, \quad 10.9, \quad 10.9
Organise these results into the following frequency table:
| Score (in litres) | Class Centre | Frequency |
|---|---|---|
| 9 - 9.4 | ||
| 9.5 - 9.9 | ||
| 10 - 10.4 | ||
| 10.5 - 10.9 |
How many times did Lachlan measure the fuel consumption?
State the modal class.
Construct a frequency histogram for the data.
Using the class centres, estimate the average fuel usage per trip to two decimal places.
The data below represents the life expectancy, in years, for various countries:
65,\, 74,\, 74,\, 69,\, 74,\, 77,\, 62,\, 63,\, 49,\, 69,\, 79,\, 51,\, 63,\, 56,\, 55,\, 72,\, 50,\, 64,\, 51,\, 47
Find the average lifespan amongst these countries.
Determine the set of seven class intervals that would be appropriate to analyse this data.
Construct a grouped frequency table with the class intervals from (b) and a class centre column.
Using the class centres estimate the average life expectancy amongst these countries.
Find the difference between the two averages calculated in part (a) and part (d).
The mass of thirty apples, rounded to the nearest gram, from an orchard were measured and recorded below:
Mass (in grams)
86, \quad 91, \quad 96, \quad 100, \quad 105, \quad 110, \quad 116, \quad 102, \quad 106, \quad 111,
119, \quad 87, \quad 94, \quad 98, \quad 102, \quad 106, \quad 113, \quad 93, \quad 96, \quad 103,
106, \quad 114, \quad 108, \quad 99, \quad 104, \quad 109, \quad 95, \quad 103, \quad 101, \quad 104
State the mass of the smallest recorded apple.
State the mass of the largest recorded apple.
Find a suitable class interval width.
Create a frequency table for this set of data.
The mass in grams of fifty laboratory rats are shown below:
391, \quad 401, \quad 379, \quad 419, \quad 382, \quad 433, \quad 412, \quad 321, \quad 359, \quad 407,
400, \quad 415, \quad 365, \quad 344, \quad 424, \quad 461, \quad 429, \quad 399, \quad 406, \quad 347,
423, \quad 364, \quad 413, \quad 393, \quad 391, \quad 383, \quad 388, \quad 436, \quad 394, \quad 452,
385, \quad 406, \quad 354, \quad 397, \quad 447, \quad 384, \quad 332, \quad 376, \quad 370, \quad 318,
351,\quad 432,\quad 391,\quad 436,\quad 379,\quad 418,\quad 369,\quad 446,\quad 345,\quad 416
Select the most suitable class interval width from the following:
5 \text{ g}
20 \text{ g}
50 \text{ g}
100 \text{ g}
Create a frequency table for this set of data.
How many rats are in the most frequent mass category?
How many rats are at least 400\text{ g}?
The level of mercury in 40 fishing waters was tested and recorded in the following stem and leaf plot:
Why would it be inappropriate to organise this data into a frequency distribution table with individual scores?
Construct a grouped frequency table for the data with a class centre column
Use the class centres to estimate the mean level of mercury detected.
Is the mean calculated from the grouped data going to be equivalent to the mean calculated from the individual scores?
What was the median level of mercury detected?
| Leaf | |
|---|---|
| 9 | 0\ 2\ 3\ 4\ 5\ 8\ 8 |
| 10 | 1\ 1\ 3\ 4\ 4\ 4\ 5\ 5\ 7\ 7\ 8\ 8\ 9\ 9 |
| 11 | 0\ 3\ 3\ 4\ 5\ 5\ 5\ 6\ 8 |
| 12 | 1\ 5\ 5\ 5\ 6\ 6\ 6\ 8\ 9\ 9 |
Key: 2 \vert 3 = 23
A survey was conducted which asked 30 people how many books they had read in the past month. Based on the frequency table provided, state whether the following statements are correct:
11 people have read from 6 to 10 books in the past month.
28 people have read at most 15 books in the past month.
We cannot determine from the table how many people have read exactly 12 books.
We can determine that 2 people have read exactly 5 books in the past month.
| Number of books read | Frequency |
|---|---|
| 1-5 | 2 |
| 6-10 | 11 |
| 11-15 | 15 |
| 16-20 | 2 |
A tree farmer measured the height of a newly planted sapling to the nearest centimetre. The results are given below:
16,\, 17,\, 27,\, 36,\, 16,\, 27,\, 22,\, 37,\, 17,\, 17,\, 26,\, 22,\, 37,\, 27,\, 22,\, 21,\, 26,\, 27,\, 37,\, 31, \\\\27,\, 37,\, 27,\, 21,\, 22,\, 32,\, 32,\, 36,\, 17,\, 32,\, 31,\, 37,\, 27,\, 26,\, 37,\, 32,\, 36,\, 27,\, 26
Find the range.
Construct a grouped frequency table with a class centre column.
Use the class centres to estimate the mean, correct to two decimal places.
In which class interval does the median lie?
State the modal class.
Calculate the percentage of saplings that are at least 25 \text{ cm} tall to one decimal place.
Calculate the percentage of saplings that have a height lower than 25 \text{ cm} to one decimal place.
The following frequency table shows the average time spent travelling to work for fifty people:
| Commute time (minutes) | Frequency |
|---|---|
| 0\leq \text{time} \lt 20 | 14 |
| 20\leq \text{time} \lt 40 | 16 |
| 40 \leq \text{time} \lt60 | 10 |
| 60 \leq \text{time} \lt 80 | 7 |
| 80\leq \text{time} \lt 100 | 3 |
| \text{Total} | 50 |
Construct a histogram to display the data shown in the frequency table.
Determine whether the following statements about the data are accurate:
The data shows that most people travel to work by car or by walking, since most travel times are fairly short, and only a few people travel by bus or train.
The data suggests that people prefer a shorter commute to work. A majority live within 40 minutes travel, and in general the longer the commute the less people there are in that category.
The data suggests that people don't care too much about how far away from work they live. Roughly equal portions of people live less than 40 minutes away and more than 40 minutes away.
The data shows that everyone lives within an hours travel from their work, with the peak amount of people living between 20 and 40 minutes away.
The following frequency table shows the price of the most recent book that seventy two university students bought:
Construct a histogram to display the data shown in the frequency table.
Which groups represent peaks in the data set?
Describe what the data shows regarding the price university stundents generally pay for their books.
| \text{Price }( \$ ) | \text{Frequency} |
|---|---|
| 0-19 | 6 |
| 20-39 | 20 |
| 40-59 | 12 |
| 60-79 | 6 |
| 80-99 | 19 |
| 100-119 | 9 |
| \text{Total} | 72 |
Consider the histogram below, showing the length of the phone calls made by Pauline in a month.
Create a frequency table for this set of data.
Pauline's phone company charges phone calls as if they were at the upper boundary of the interval. For example, a phone call lasting 1 minute and 48 seconds would be charged as if it were a 2 minute call.
Find the total number of minutes for which Pauline will be charged for phone calls this month.
If Pauline receives 30 minutes of free calls per month, and is charged \$1.50 per minute afterwards, find her total spending for the month.
Explain why a pie chart is inappropriate for the data shown below:
What feature is misleading about the following line graph?
Consider the following line graph:
Source: Brookings report on American education.
The bottom section of the graph has been cropped. Describe the effect this may have on interpreting the graph.
The labels on the horizontal axis are not evenly spaced. Explain why this may be misleading.
Consider the given column graph:
Why is this a particularly poor example of a graph with broken axes?
Explain why it is not generally good practice to use a vertical scale with a broken axis for column graphs.
Describe a graphical display that would be better suited to this situation.
Consider the following line graph:
What feature is missing from the graph?
Explain why this might be misleading.
Consider the following line graphs of the same set of sales figures:
Describe how the difference in scale between the two graphs might be misleading.