10.01 Summarising data
Classify the kind of data these surveys will collect as one of the following:
- Categorical
- Discrete numerical
- Continuous numerical
A class was surveyed about what kinds of pet they own.
A class was surveyed about how many apps they have on their phone.
A class was surveyed about how long they spent on homework last night.
Determine whether the following classify as numerical or non-numerical data:
Favourite flavours
Maximum temperature
Daily temperature
Types of horses
Amount owing on layby
Types of vegetables
Brands of tablets
Types of folders
Daily UV index
Maximum rainfall
Favorite colours
Colours of folders
Brands of phones
Determine whether the following classify as categorical or non-categorical data:
Maximum snowfall
Daily UV index
Types of dogs
Favorite colours
Amount owing on a purchase
Brands of phones
Types of fruits
Colours of folders
For each of these numerical data types, identify whether they are discrete or continuous:
Number of classrooms at a school
Daily humidity
The ages of a group of people in years
The time taken to run 200 metres
Lengths of cats' whiskers
The distance from Earth to Mars
How long it takes to fall asleep
Amount paid for walking the dog
The number of people taller than you
The top speed of different motorcycles
The size a coin collection
The amount of soda you drink in a day
The best time for solving a Rubik's cube
The hourly pay rate for a particular job
Number of views of a YouTube channel
The snowfall in your city
Number of children in your sports team
The strength of an earthquake
Amount of money owing on a mortgage
Your marks in a Physics test
Find the mean of the following scores:
9, 5, 2, 3, 1
3, 2, 5, 1, 4
4, 5, 6, 7, 3
4, 8, 2, 5, 1
Find the mean of the following scores:
1, 3, 7, 5, 2
7, 4, 3, 4, 8
9.5, 7.1, 8.8, 2.5, 1.7
- 2 , - 8 , - 9 , - 4 , - 7
- 9 , 0, 9, - 6 , 6
6.2, 6.1, 6.1, 6.9, 6.7
0.1,-0.1,0.2,0.3,-0.5
-10.5, -5.4, -6.8, -5.2, -3.2
56, 89, 95, 71, 75, 84, 65, 83
-14, 0, -2, -18, -8, 0, -15, -1
The following five numbers have a mean of 11:
11, 13, 9, 13, 9
If a new number is added that is smaller than 9, will the mean will be higher or lower?
The following six numbers have a mean of 107:
102, 103, 111, 107, 108, 111
If a new number is added that is larger than 111, will the mean will be higher or lower?
The mean of a set of scores is 35 and the sum of the scores is 560. Calculate the number of scores.
There are five numbers with a mean of 7. If four of the numbers are 10, 10, 8, 7, find the fifth number.
The five numbers 16, 16, 17, 24 \text{ and } 17 have a mean of 18. If a new number is added that is bigger than 24, state whether the mean will become higher or lower.
The mean of a set of 41 scores is 18.6. If a score of 71.8 is added to the set, find the new mean. Round your answer to two decimal places.
For the following sets of scores:
Sort the scores in ascending order.
Find the median.
17, 8, 6, 11, 9, 18
69.4,66.7,46.6,76.6,52.8,80.6, 63.9
44.9,45.6, - 54.8,74.7, - 77.6, -42.6,67.9,40.6
Find the median of the following scores:
9, 7, 6, 8, 2
4, 13, 10, 19, 18, 5
3.2, 2.3, 5.5, 4.6, 8.5
47.4, 22.2, 39.2, 46.2, 38.4, 35.4
- 4 , - 17 , - 11 , 14, 20, 6
-1.5, -2.5, -3, -2, -5, -6
In a set of 152 scores, between which two scores does the median lie?
A set of 69 scores is arranged in ascending order. In what position does the median score lie?
Write down 4 consecutive odd numbers whose median is 40.
Find the mode of the following scores:
6, 1, 8, 1, 6, 9, 7, 6, 8
1.4, 4.2, 7.4, 7.4, 3.5, 1.4, 7.4, 3.5, 3.4
- 7 , - 6 , - 2 , - 9 , - 2 , - 8 , - 7 , - 9 , - 9
-0.5, -0.2, -0.3, -1.2, -0.5, -0.7, -0.7, -0.5
102, 100, 103, 102, 104, 103, 100, 103
- 12 , - 12 , - 6 , - 9 , - 7 , - 8 , - 7 , - 9 , - 7
Find both modes of the following set of scores:2, \, 2, \, 6, \, 8, \, 8, \, 8, \, 8, \, 12, \, 14, \, 14, \, 14, \, 14, \, 18, \, 18
Explain why the following data set does not have a mode:
4, \, 8, \, 1, \, 2, \, 5, \, 9, \, 3, \, 6Find the range of the following scores:
7, 12, 9, 19, 11, 4, 8, 15, 3
11.9, 15.6, 3.7, 19.6, 18.3, 4.7, 9.1, 12.5, 5.4
- 16 , - 3 , - 12 , - 8 , - 11 , - 15 , - 18 , - 5 , - 17
11, - 19 , 14, 17, - 11 , 15, 13, - 5 , - 20
Find the range of the following scores:
10, 7, 2, 14, 13, 15, 11, 4
15, - 2 , - 8 , 8, 15, 6, - 16 , 15
- 0.5537 , 1.7444, - 0.3381 , 0.7200, - 0.3381 , 1.0435
A group of students had a range in marks of 17 and the lowest score was 9. Find the highest score in the group.
The range of a set of scores is 8, and the highest score is 19. Find the lowest score in the set.
A rating system of 1 - 3 was used in a survey to determine the usefulness of a new feature. The ten scores shown below are known to have a mode of 1.
3, 2, 3, 2, 1, 3, 1, 1, 2, xFind the missing score, x.
A real estate agent wanted to determine a typical house price in a certain area. He gathered the selling price of some houses (in dollars):
317\,000, \text{ }\text{ }320\,000,\text{ }\text{ } 347\,000,\text{ }\text{ } 360\,000,\text{ }\text{ } 378\,000,\text{ }\text{ } 395\,000,\text{ }\text{ } 438\,000,\text{ }\text{ } 461\,000,\text{ }\text{ } 479\,000,\text{ }\text{ } 499\,000
Calculate the mean house price.
Determine the median house price.
Oprah has been growing watermelons. The weights of the watermelons (in kilograms) are: 15,\text{ }\text{ } 6,\text{ }\text{ } 5,\text{ }\text{ } 2,\text{ }\text{ } 4,\text{ }\text{ } 4,\text{ }\text{ } 5
Calculate the median weight of the watermelons.
Calculate the mean weight. Round your answer to two decimal places.
Durations of calls (in minutes) made in a household were recorded as follows:
5,\text{ }\text{ } 11,\text{ }\text{ } 3,\text{ }\text{ } 9,\text{ }\text{ } 5,\text{ }\text{ } 14,\text{ }\text{ } 5,\text{ }\text{ } 14,\text{ }\text{ } 14,\text{ }\text{ } 3,\text{ }\text{ } 7,\text{ }\text{ } 7,\text{ }\text{ } 7,\text{ }\text{ } 5,\text{ }\text{ } 3,\text{ }\text{ } 3,\text{ }\text{ } 7,\text{ }\text{ } 14,\text{ }\text{ } 5
What was the total number of calls made?
What was the longest duration of a call?
What was the shortest duration of a call?
What was the mean duration of a call? Round your answer to two decimal places.
What was the modal duration?
What was the median duration?
Marge grows two different types of bean plants. She records the number of beans that she picks from each plant for 10 days. Her records are as follows:
-
Plant A: 10, \text{ } 4,\text{ } 4, \text{ }5, \text{ }7, \text{ }10,\text{ } 3,\text{ } 3,\text{ } 9,\text{ } 10
Plant B: 8,\text{ } 7,\text{ } 5,\text{ } 5,\text{ } 9,\text{ } 7,\text{ } 8,\text{ } 7,\text{ } 5,\text{ } 6
What is the mean number of beans picked per day for Plant A? Round your answer to one decimal place.
What is the mean number of beans picked per day for Plant B? Round your answer to one decimal place.
What is the range for Plant A?
What is the range for Plant B?
Which plant produces more beans on average?