State whether the scores in each graph can be described as positively skewed, negatively skewed or symmetrical:
| 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 |
The table shows the number of crime novels in a bookshop for different price ranges.
| \text{Price of crime novel, to the nearest } \$5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 |
|---|---|---|---|---|---|---|---|
| \text{Frequency} | 3 | 9 | 19 | 6 | 19 | 9 | 3 |
Plot this data as a bar graph.
Describe the shape of the data in the graph.
For each of the following graphs:
Are there any outliers? If so, state them.
Are there any clusters? If so where?
What is the mode?
Describe the distribution 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 | 2 = 12
| Leaf | |
|---|---|
| 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 | 2 = 52\text{ hours}
For each of the graphs below:
Describe the shape of the distribution.
Determine the lower quartile score and the upper quartile Score.
Hence, calculate the interquartile range.
Using the interquartile range, are there any outliers in the data set? If so, what are they?
How many peaks are there on the following dot plot?
Describe the distribution of the following graphs:
The given stem and leaf plot shows the age of people to enter through the gates of a concert in the first 5 seconds:
What was the median age?
What was the difference between the lowest age and the median?
What is the difference between the highest age and the median?
What was the mean age? Give your answer 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 \text{ years old}
Consider the given histogram, representing students' heights in centimetres:
Does the histogram most likely represent grouped data or individual scores? Explain your answer.
The stem and leaf plot shows the batting scores of two cricket teams, England and India.
What is the highest score from England?
What is the highest score in India?
Find the mean score of England.
Find the mean score of India.
Calculate the combined mean of the two teams.
| England | India | |
|---|---|---|
| 1\ 0 | 3 | 1\ 2\ 4\ 7 |
| 6\ 6\ 5\ 5\ 5\ 5 | 4 | 0\ 2\ 9 |
| 7\ 3 | 5 | 2\ 5 |
| 6 | 4 |
Key: 1 | 2 = 12
Consider the frequency distribution table :
| \text{Score, }x | \text{Frequency, }f | fx |
|---|---|---|
| 4 | 11 | |
| 5 | 35 | |
| 16 | ||
| 14 | ||
| \text{Total:} | 43 | 365 |
Complete the table.
Find the mean of the scores, correct to two decimal places.
Find the mode of the scores.
Find the range of the scores.
How many scores are less than the mode?
Consider the dot plot given. From which score can a dot be removed so that the mean, median and mode remain unchanged?
Which of the following dot plots have the highest median?
For the following scenarios, determine the value of the x:
A rating system of 1 - 4 was used in a survey to determine the usefulness of a new feature. The 14 scores shown below are known to be bi-modal with values 2 \text{ and }4.
2,\quad 4,\quad 2,\quad 4,\quad 3,\quad 2,\quad 3,\quad 4,\quad 4,\quad 1,\quad 1,\quad 2,\quad 3,\quad xA rating system of 1 - 3 was used in a survey to determine the usefulness of a new feature. The 10 scores shown below are known to have a mode of 1.
3,\quad 2,\quad 3,\quad 2,\quad 1,\quad 3,\quad 1,\quad 1,\quad 2,\quad xThe six numbers 6, 2, 7, 18, 17 and an unknown number x have a median of 8.5. Find the value of x.
Five numbers have a range of 16, a mode of 2, a median of 7 and a mean of 8. The minimum number in the set is 2. Calculate:
The minimum
The median
The maximum
Three numbers have a mode of 10 and a mean of 10. Write the three numbers of the data set.
Four numbers have a range of 5, a median of 9 and a mode of 11. Write the four numbers of this data set.
Find the most appropriate measure of centre for the following data set:
15,\quad 13,\quad 16,\quad 17,\quad 15,\quad 15,\quad 15
8,\quad 10,\quad 14,\quad 18,\quad 19,\quad 91
Susanah has been growing watermelons. The weight of the watermelons (in kilograms) are shown below:15,\quad 6,\quad 5,\quad 2,\quad 4,\quad 4,\quad 5
Calculate the median weight of Oprah's watermelons.
Calculate the mean weight of Oprah's watermelons. Round your answer to two decimal places if necessary.
Find the most appropriate measure of centre of this data set.
Consider the histogram below:
Determine the measure of centre that would be most appropriate to use to represent the data in this graph. Explain your answer.
A timed quiz consists of 6 puzzles. The data below shows the times (in seconds) that it took Sophia to complete each question on her first and second attempts of the quiz:
Times in first attempt: \quad 11,\quad 15,\quad 17,\quad 20,\quad 23,\quad 34
Times in second attempt: \quad 20,\quad 20,\quad 20,\quad 19,\quad 21,\quad 20
Calculate the mean time spent on each puzzle in the first attempt.
Calculate the mean time spent on each puzzle in the second attempt.
For which of Sophia's attempts would the mean number of minutes spent per question be a better indicator of her performance than the median number of minutes spent per question? Explain your answer.
The price of petrol at a petrol station was recorded each day for two weeks. The results are presented in the table below:
| Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday | |
|---|---|---|---|---|---|---|---|
| Week 1 | \$1.70 | \$1.50 | \$1.62 | \$1.46 | \$1.49 | \$1.46 | \$1.55 |
| Week 2 | \$1.25 | \$1.36 | \$1.25 | \$1.21 | \$1.21 | \$1.20 | \$3.30 |
The mean petrol price across the 14 days of records is \$1.54 per litre. For which week is this mean a better indication of the price of petrol? Explain your answer.
Every week over 45 weeks, a kayaking club ran social sessions and the number of people who attend who attended each session was recorded in the table:
| Number of people attending | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
|---|---|---|---|---|---|---|---|---|---|
| Number of weeks | 6 | 5 | 6 | 5 | 6 | 5 | 6 | 5 | 6 |
Explain why the mean and the median are equally accurate indicators of the typical number of people who attended each session.
The histograms below represents the luggage weight of each passenger on board an airline's morning and afternoon flight:
The airline wants to get an indication of how much luggage each passenger is checking in. For which flight's data would the median be a more precise indicator of a typical passenger's luggage weight than the mean? Explain your answer.