# Chapter 2 Summarising Numerical Data

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These questions are based on Chapter 2 from the book. They test your ability to complete calculations, and become part of the evidence of your abilities. This test is used in conjunction with your SAC grades to provide an 'S' or 'N' grade in this subject.

• 1.

### From the image above, which statement is most correct?

• A.

The mean and mode are the same

• B.

The median value is higher than the mean

• C.

The mean value is higher than the median

• D.

The mean and median are approximately the same

B. The median value is higher than the mean
Explanation
The median value is higher than the mean when the data is skewed to the left, meaning that there are a few extremely high values that pull the mean up. In this case, the majority of the data is clustered towards the lower end, causing the median to be higher than the mean.

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• 2.

### From the image above, which statement is most correct?

• A.

The mean and mode are the same

• B.

The median value is higher than the mean

• C.

The mean value is higher than the median

• D.

The mean and median are approximately the same

B. The median value is higher than the mean
• 3.

### From the image above, which statement is most correct?

• A.

The mean and mode are the same

• B.

The median value is higher than the mean

• C.

The mean value is higher than the median

• D.

The mean and median are approximately the same

C. The mean value is higher than the median
Explanation
The mean value is higher than the median because the mean is calculated by adding up all the values and dividing by the total number of values, while the median is the middle value when the data is arranged in ascending or descending order. If the data is skewed towards higher values, the mean will be higher than the median.

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• 4.

### From the image above, which statement is most correct?

• A.

The mean and mode are the same

• B.

The median value is higher than the mean

• C.

The mean value is higher than the median

• D.

The mean and median are approximately the same

D. The mean and median are approximately the same
Explanation
The mean is the average of all the values in a dataset, while the median is the middle value when the data is arranged in ascending or descending order. If the mean and median are approximately the same, it suggests that the dataset is symmetrically distributed without any extreme outliers.

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• 5.

### From the image above, which statement is most correct?

• A.

The mean and mode are the same

• B.

The median value is higher than the mean

• C.

The mean value is higher than the median

• D.

The mean and median are approximately the same

C. The mean value is higher than the median
Explanation
The mean is calculated by summing all the values in a dataset and dividing by the number of values, while the median is the middle value when the data is arranged in ascending or descending order. If the mean value is higher than the median, it suggests that there are some larger values in the dataset that are pulling the mean upwards, indicating a right-skewed distribution.

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• 6.

### From the image above, which statement is most correct?

• A.

The mean and mode are the same

• B.

The median value is higher than the mean

• C.

The mean value is higher than the median

• D.

The mean and median are approximately the same

C. The mean value is higher than the median
Explanation
The mean is calculated by summing up all the values in a dataset and then dividing by the total number of values. The median is the middle value in a dataset when it is arranged in ascending or descending order. If the mean is higher than the median, it suggests that there are some larger values in the dataset that are pulling the mean up. This indicates that the distribution of the data is skewed towards the higher values. Therefore, the statement "The mean value is higher than the median" is most correct.

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• 7.

### From the image above, which statement is most correct?

• A.

The mean and mode are the same

• B.

The median value is higher than the mean

• C.

The mean value is higher than the median

• D.

The mean and median are approximately the same

C. The mean value is higher than the median
Explanation
The mean value is higher than the median because the mean is calculated by summing all the values and dividing by the total number of values, while the median is the middle value when the data is arranged in ascending or descending order. If the data set has outliers or extreme values, it can skew the mean, causing it to be higher or lower than the median. Therefore, in this case, the mean value is higher than the median.

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• 8.

### From the image above, which statement is most correct?

• A.

The mean and mode are the same

• B.

The median value is higher than the mean

• C.

The mean value is higher than the median

• D.

The mean and median are approximately the same

C. The mean value is higher than the median
Explanation
The mean value is higher than the median when the data set has outliers or extreme values that pull the mean away from the center. In this case, the mean is influenced by these extreme values, causing it to be higher than the median. The median, on the other hand, is less affected by outliers and represents the middle value of the data set. Therefore, the statement "The mean value is higher than the median" is most correct based on the given information.

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• 9.

### From the image above, which statement is most correct?

• A.

The mean and mode are different

• B.

The median value is higher than the mean

• C.

The mean value is higher than the median

• D.

The mean and median are approximately the same

D. The mean and median are approximately the same
Explanation
The mean is the average value of a set of numbers, while the median is the middle value when the numbers are arranged in ascending or descending order. If the mean and median are approximately the same, it suggests that the data is symmetrically distributed. This means that there are an equal number of values above and below the middle value, resulting in a similar average and middle value.

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• 10.

### From the image above, which statement is most correct?

• A.

The mean and mode are the same

• B.

The median value is higher than the mean

• C.

The mean value is higher than the median

• D.

The mean and median are approximately the same

B. The median value is higher than the mean
Explanation
The median value is higher than the mean when the data is skewed to the left, meaning that there are a few extremely low values that pull the mean down. In this case, the majority of the values are higher than the mean, causing the median to be higher.

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• 11.

### From the image above, which statement is most correct?

• A.

The mean and mode are the same

• B.

The median value is higher than the mean

• C.

The mean value is higher than the median

• D.

The mean and median are approximately the same

B. The median value is higher than the mean
Explanation
The median value is higher than the mean when there are a few extremely high values in the data set. This is because the median is not affected by outliers, while the mean is influenced by them. Therefore, if the median is higher than the mean, it suggests that there are some unusually high values pulling the median up.

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• 12.

### From the image above, which statement is most correct?

• A.

The mean and mode are the same

• B.

The median value is higher than the mean

• C.

The mean value is higher than the median

• D.

The mean and median are approximately the same

C. The mean value is higher than the median
Explanation
The mean value is higher than the median because the mean is calculated by summing all the values and dividing by the total number of values, while the median is the middle value in a sorted list of values. If the distribution is skewed towards higher values, the mean will be pulled up, resulting in a higher mean than the median.

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• 13.

20
• 14.

12
• 15.

### I collected data about average temperature in spring from 30 participants. I added the values together and they totalled 540 For this set of data, what is the value of :

18
Explanation
The value of 18 represents the average temperature in spring collected from the participants. The total sum of the temperatures collected from the 30 participants is 540, which means that the average temperature can be calculated by dividing the total sum by the number of participants (30). Therefore, the average temperature in spring is 18.

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• 16.

### I collected data about height of a junior sports team from 30 participants. I added the values together and they totalled 4950 For this set of data, what is the value of :

165
Explanation
The value of 165 represents the height of one participant in the junior sports team. The data collected from 30 participants was added together to obtain a total of 4950, which means that the average height of the team is 165.

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• 17.

### I collected data about number of radios in a house from 40 participants. I added the values together and they totalled 360 For this set of data, what is the value of :

9
Explanation
The value of 9 represents the number of radios in a house. The data collected from 40 participants was added together and the total was 360. This means that the sum of all the individual values for the number of radios in each house is 360. Therefore, the value of 9 represents one of the individual data points, indicating that there were 9 radios in one of the houses.

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• 18.

### I collected data about weight of sheep from 20 participants. I added the values together and they totalled 1440 For this set of data, what is the value of :

72
Explanation
The value of 72 is the weight of a single sheep in the given set of data. This can be determined by dividing the total weight of all the sheep (1440) by the number of sheep (20).

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• 19.

### I collected data about height of potted plants from 80 participants. I added the values together and they totalled 1200 For this set of data, what is the value of :

15
Explanation
The value of 15 represents the height of a potted plant in the collected data. Since the total height of all the potted plants is 1200, it implies that there is at least one potted plant with a height of 15 in the dataset.

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• 20.

### I collected data about number of people in a family from 22 participants. I added the values together and they totalled 110 For this set of data, what is the value of :

5
Explanation
The value of 5 is the number of people in a family. Since the total number of people in the 22 families is 110, it means that on average each family consists of 5 people.

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• 21.

12
• 22.

### I collected data about age of graduate from a masters degree from 15 participants. I added the values together and they totalled 375 For this set of data, what is the value of :

25
Explanation
The value of 25 refers to the age of a graduate from a master's degree program. This information is not explicitly stated in the question, but it can be inferred based on the context of collecting data about the age of graduates. Since the total of the collected data is 375, it is reasonable to assume that one of the participants in the study is 25 years old.

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• 23.

### I collected data about age of university students from 17 participants. I added the values together and they totalled 340 For this set of data, what is the value of :

340
Explanation
The value of 340 is the sum of the ages of the 17 university students.

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• 24.

### I collected data about shirt size for women from 9 participants. I added the values together and they totalled 108 For this set of data, what is the value of :

108
Explanation
The value of 108 is the sum of the shirt sizes for women collected from the 9 participants.

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• 25.

540
• 26.

### I collected data about height of a junior sports team from 30 participants. I added the values together and they totalled 4950 For this set of data, what is the value of :

4950
Explanation
The value of 4950 is the sum of the heights of the 30 participants in the junior sports team.

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• 27.