Describe the shape of the data in the following graphs:
| Leaf | |
|---|---|
| 1 | 6\ 7\ 7 |
| 2 | 2\ 2\ 2\ 2\ 3\ 3\ 3 |
| 3 | 3\ 3\ 3\ 6\ 6\ 6\ 7\ 7\ 7\ 7\ 7 |
| 4 | 4\ 4\ 4\ 4\ 4\ 4 |
| 5 | 7\ 7 |
Key: 2 \vert 3 = 23
Determine whether the following graphs are bimodal:
| Leaf | |
|---|---|
| 1 | 0\ 0\ 2\ 7 |
| 2 | 2\ 2\ 3\ 3\ 5\ 8 |
| 3 | 1\ 6\ 4 |
| 4 | 7 |
| 5 | 0\ 1\ 6 |
| 6 | 5\ 7\ 7\ 8\ 8 |
| 7 | 4\ 4\ 4 |
| 8 | 4\ 4 |
Key: 2 \vert 3 = 23
| Leaf | |
|---|---|
| 1 | 2\ 3\ 4\ 5\ 5\ 6\ 6\ 7\ 7\ 9 |
| 2 | 1\ 2\ 4\ 4 |
| 3 | 0\ 2\ 9\ 9 |
| 4 | |
| 5 | 5 |
Key: 1\vert 2=12
How would you describe the modality of the following dot plot? Explain your answer.
The table shows the number of crime novels in a bookshop for different price ranges rounded off to the nearest \$ 5:
Graph this data as a histogram.
Describe the shape of the distribution of the data.
| Price of crime novel | Frequency |
|---|---|
| \$5 | 5 |
| \$10 | 10 |
| \$15 | 17 |
| \$20 | 8 |
| \$25 | 17 |
| \$30 | 10 |
| \$35 | 5 |
The number of hours worked per week by a group of people is represented in the following stem-and-leaf plot:
State the value of any outliers.
Is there any clustering of data? If so, in what interval?
State the mode.
| Leaf | |
|---|---|
| 0 | 2 |
| 1 | |
| 2 | |
| 3 | 0\ 3\ 6\ 6 |
| 4 | 1\ 4\ 5\ 6\ 6\ 7 |
| 5 | 0\ 4\ 6\ 7\ 9 |
| 6 | 0 |
Key: 2 \vert 3 = 23
Consider the stem plot given:
State the value of any outliers.
Is there any clustering of data? If so, in what interval?
State the mode.
Describe the shape of the distribution.
| Leaf | |
|---|---|
| 0 | 5 |
| 1 | 7\ 8 |
| 2 | 0\ 8 |
| 3 | 1\ 3\ 3\ 7\ 8\ 9 |
| 4 | 1\ 3\ 5\ 8\ 8\ 8 |
| 5 | |
| 6 | |
| 7 | |
| 8 | |
| 9 | 2 |
Key: 2 \vert 3 = 23
Temperatures were recorded over a period of time and presented as a dot plot:
Are there any outliers?
Is there any clustering of data? If so, in what interval?
What is the modal temperature?
Describe the shape of the distribution.
The number of peanuts in mixed nut packets were sampled and recorded in the following stem plot:
Complete the frequency distribution table:
| Score | Frequency |
|---|---|
| 40-49 | |
| 50-59 | |
| 60-69 | |
| 70-79 | |
| 80-89 | |
| 90-99 | |
| 100-109 | |
| 110-119 |
| Leaf | |
|---|---|
| 4 | 3\ 6\ 8 |
| 5 | 1\ 2\ 2\ 6\ 7\ 7\ 8 |
| 6 | 0\ 0\ 2 |
| 7 | 3\ 3\ 4\ 5\ 9 |
| 8 | 1\ 1\ 1\ 4\ 6\ 8\ 8\ 9 |
| 9 | 0\ 2\ 5\ 6 |
| 10 | 1\ 2\ 3\ 5\ 5\ 6\ 7\ 8 |
| 11 | 0\ 4\ 5\ 7 |
Key: 5 | 2 = 52
Describe the modaility of the distribution.
State the modal class or classes of the data.
The percentage of faulty computer chips in 42 batches were recorded in the given histogram:
Describe the modaility of the distribution.
State the modal class or classes of the data.
Consider the dot plot below:
Are there any outliers?
Is there any clustering of data?
State the modal score(s).
Describe the shape of the distribution.
Consider the data shown in the graph:
Are there any outliers?
Is there any clustering of data? If so, in what interval?
State the mode.
Describe the shape of the distribution.
The reaction time of drivers was tested and recorded in the dot plot below:
Construct a frequency distribution table for the individual data values.
Describe the modaility of the distribution.
State the mode(s).
Estimate the value of the mean of the following data set correct to one decimal place:
Consider the histogram representing students' heights in centimetres:
Does the histogram most likely represent grouped data or individual scores?
Estimate the value of the mean to one decimal place.
Describe the shape of the distribution.
Consider the given column graph:
Describe the shape of the distribution.
Find the following:
Lower quartile
Upper quartile
Hence, calculate the interquartile range.
Are there any outliers? If so, state the value.
Consider the dot plot given:
Describe the shape of the distribution.
Find the following:
Lower quartile
Upper quartile
Hence, calculate the interquartile range.
Are there any outliers? If so, state the value.
The stem-and-leaf plot below shows the age of people to enter through the gates of a concert in the first 5 seconds:
Find the median age.
Find the difference between the lowest age and the median.
Find the difference between the highest age and the median.
Calculate the mean age, correct to two decimal places.
Is the data positively or negatively skewed?
| Leaf | |
|---|---|
| 1 | 0\ 1\ 2\ 2\ 3\ 3\ 4\ 4\ 4\ 8\ 8\ 8 |
| 2 | 1\ 7 |
| 3 | 4\ 5\ 5 |
| 4 | 0 |
| 5 | 4 |
Key: 1 | 2 \ = \ 12 years old
\text{VO}_2 \text{Max} is a measure of how efficiently your body uses oxygen during exercise. The more physically fit you are, the higher your \text{VO}_2 \text{Max}. Here are some people's results, listed in ascending order, when their \text{VO}_2 \text{Max} was measured:
21,\, 21,\, 23,\, 25,\, 26,\, 27,\, 28,\, 29,\, 29,\, 29,\, 30,\, 30,\, 32,\, 38,\, 38,\, 42,\, 43,\, 44,\, 48,\, 50,\, 76
Determine the median \text{VO}_2 \text{Max}.
Determine the upper quartile value.
Determine the lower quartile value.
Consider the box plot for this data set and state whether the results are positively or negatively skewed.
State the value of the outlier.
An average untrained healthy person has a \text{VO}_2 \text{Max} between 30 and 40. What can we say about the exercise habits of the majority of this group of people?
Match the histograms on the left to the corresponding box plots on the right:
Histogram A
Histogram B
Histogram C
Histogram D
Histogram E
Histogram F
Construct a box plot for the following histograms:
State whether the following pairs of histograms and box plots are correctly matched with respect to their shape:
Explain why the following pairs of histograms and box plots do not match:
