11.03 Shape of data
A set of data is strongly positively skewed. If the median is 60, is the mean less than, equal to or greater than 60?
Determine whether the following graphs are bimodal:
Determine whether the following graphs are positively skewed, negatively skewed or symmetrical:
Find the mean of this data set correct to two decimal places.
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 following:
Median age.
Difference between the lowest age and the median.
Difference between the highest age and the median.
The mean age, correct to two decimal places.
Is the data positively or negatively skewed?
| Leaf | |
|---|---|
| 1 | 0\ 1\ 2\ 3\ 4\ 5\ 6\ 6 |
| 2 | 0\ 1\ 1\ 2\ 2\ 5 |
| 3 | 4\ 7\ 9 |
| 4 | 4 |
| 5 | 1 |
Key: 1 | 2 = 12 years old
The number of hours worked per week by a group of people is represented in the given stem-and-leaf plot:
Are there any outliers? If so, state the value.
Is there any clustering of data? If so, in what interval?
Find the modal class(es).
| No. of hours | |
|---|---|
| 0 | 2 |
| 1 | |
| 2 | 0\ 3\ 6\ 6 |
| 3 | 1\ 4\ 5\ 6\ 6\ 7 |
| 4 | 0\ 4\ 6\ 7\ 9 |
| 5 | 0 |
Key: 5 \vert 2 = 52 \text{ hours}
Consider the given stem-and-leaf plot:
Are there any outliers? If so, state the value.
Is there any clustering of data? If so, in what interval?
Find the modal class(es).
Describe the shape of the data.
| 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: 1 \vert 2 = 12
The table shows the number of crime novels in a bookshop for different price ranges:
Construct a histogram using the data in the table.
Describe the shape of the data in the graph and table.
| \text{Price of crime novel} \\ \text{to nearest } \$5 | \text{Frequency} |
|---|---|
| 5 | 5 |
| 10 | 11 |
| 15 | 15 |
| 20 | 8 |
| 25 | 15 |
| 30 | 11 |
| 35 | 5 |
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 | 6\ 7\ 7\ 8\ 8 |
| 7 | 0\ 0\ 3\ 3\ 4\ 5\ 9 |
| 8 | 1\ 1\ 1\ 4\ 6\ 8\ 8\ 9 |
| 9 | 0\ 2\ 4\ 5\ 6\ 9 |
| 10 | 1\ 2\ 3\ 5\ 5\ 6\ 7\ 8 |
| 11 | 0\ 4\ 5\ 7 |
Key: 5 | 2 = 52
Determine whether the following describe the distribution of the data:
Unimodal
Bimodal
Multimodal but not bimodal
Find the modal class of the data.
The percentage of faulty computer chips in 42 batches were recorded in the given histogram:
Determine whether the following describe the distribution of the data:
Unimodal
Bimodal
Multimodal but not bimodal
Find the modal class of the data.
Consider the data shown in the given column graph:
Are there any outliers?
Is there any clustering of data?
Where does the clustering occur: 1 to 4, 5 to 7, or 8 to 11?
Find the mode.
Describe the shape of the distribution of the data.
The shoe sizes of all the students in a class were measured and the data was presented in a bar graph:
Are there any outliers?
Is there any clustering of data?
Where does the clustering occur?
Find the modal shoe size.
Describe the shape of the distribution of the data.
Consider the data shown in the histogram:
Are there any outliers? If so, what is the value?
Is there any clustering of data? If so, in what interval?
What is the mode?
Describe the shape of the distribution of the data.
Consider the dot plot shown:
Describe the shape of the distribution.
Are there any outliers? If so, state the value.
Temperatures were recorded over a period of time and presented in the given dot plot:
Are there any outliers? If so, state the value.
Is there any clustering of data? If so, in what interval?
Find the modal temperature.
Describe the shape of the data.
Consider the given dot plot:
Are there any outliers? If so, state the value.
Is there any clustering of data? If so, in what interval?
Find the modal score(s).
Describe the shape of the data.