A group of 10 has a mean of 36 and a second group of 16 has a mean of 20 Find the mean of the combined group of 26.
A group of 10 has a mean of 36 and a second group of 16 has a mean of 20 Find the mean of the combined group of 26.
To find the mean of the combined group, you can use the concept of weighted averages. Since the group sizes are different, the mean of the combined group will be influenced by the size of each group. Here’s how you can calculate it:
Let:
– Group 1 size = 10
– Group 1 mean = 36
– Group 2 size = 16
– Group 2 mean = 20
To find the mean of the combined group:
1. Calculate the total sum of the values in both groups:
Total sum = (Group 1 size * Group 1 mean) + (Group 2 size * Group 2 mean)
Total sum = (10 * 36) + (16 * 20) = 360 + 320 = 680
2. Calculate the total size of the combined group:
Total size = Group 1 size + Group 2 size = 10 + 16 = 26
3. Finally, calculate the mean of the combined group:
Mean of combined group = Total sum / Total size = 680 / 26 ≈ 26.15
The mean of the combined group of 26 is approximately 26.15.
(a) Explaining Terms with Examples:
Population:
The population refers to the entire group of individuals, items, or elements that share a common characteristic and are of interest in a study. For instance, if we want to study the average income of all households in a city, the entire set of households in that city constitutes the population.
Example: Suppose we’re conducting research on the reading habits of students in a university. The population would include all students enrolled in the university.
Statistics:
Statistics is a field of mathematics that involves collecting, analyzing, interpreting, and presenting data. It provides methods to summarize data and draw meaningful conclusions from it.
Example: A survey conducted to determine the percentage of students who use online learning resources. The calculated percentage is a statistical measure.
Non-probability Sampling:
Non-probability sampling is a method of selecting a sample from a population where not every element has an equal chance of being included. It’s often used when certain elements are difficult to access.
Example: If we’re researching students’ opinions on a new course curriculum, and we select students who are easily available in the university courtyard, it’s a non-probability sampling technique called convenience sampling.
Sampling Technique:
A sampling technique is a systematic method used to select a subset (sample) from a larger group (population) for research. Different techniques are employed based on research goals and available resources.
Example: In a study analyzing crime rates in a city, random sampling might be used, where households are selected at random to ensure a representative sample.
Sample:
A sample is a subset of individuals or items selected from a larger population for research purposes. It helps researchers make inferences about the entire population without studying each element.
Example:If we’re conducting a study on the average height of all students in a school, but we only measure the heights of a few students, those measured students form the sample.
(b) Explaining Terms:
The Mode:
The mode is the value that appears most frequently in a dataset. It’s the number that occurs with the highest frequency.
Example: Consider the dataset: 12, 18, 15, 15, 20, 22, 15, 17. Here, the mode is 15 because it appears three times, which is more frequent than any other number.
ii. The Mean:
The mean, also known as the average, is calculated by summing up all the values in a dataset and then dividing by the total number of values.
Example: Suppose we have test scores of 85, 90, 78, 92, and 88. The mean score is (85 + 90 + 78 + 92 + 88) / 5 = 86.6.
iii. The Median:
The median is the middle value in a dataset when it’s arranged in numerical order. If there’s an even number of values, the median is the average of the two middle values.
Example: For the dataset: 12, 18, 15, 20, 22, the median is 18. But for the dataset: 12, 18, 15, 20, 22, 25, the median is (18 + 20) / 2 = 19.
[mediator_tech]
Evaluation
i. The mode is the value that appears ____________ frequently in a dataset.
a) Most
b) Least
c) Equally
ii. The mean of a set of values is calculated by ____________ the sum of all values by the total number of values.
a) Dividing
b) Multiplying
c) Subtracting
iii. The median is the middle value in a dataset when arranged in ____________ order.
a) Random
b) Numerical
c) Alphabetical
iv. A group of 10 has a mean of 36, and a second group of 16 has a mean of 20. To find the mean of the combined group of 26, you need to calculate the ____________ of the values and divide by the ____________ of the combined group.
a) Sum, total size
b) Average, total sum
c) Median, mean
i. In a dataset: 5, 7, 8, 5, 9, 5, 6, the mode is ____________.
a) 5
b) 7
c) 9
ii. The mean of 14, 16, 18, and 22 is ____________.
a) 18
b) 17
c) 15
iii. In a dataset: 10, 12, 18, 14, 20, the median is ____________.
a) 10
b) 14
c) 18
iv. Given a group of 20 with a mean of 25 and another group of 30 with a mean of 40, to find the mean of the combined group of 50, you’d calculate the ____________ of the values and divide by the ____________ of the combined group.
a) Average, total size
b) Sum, total size
c) Mean, total sum
i. If a dataset has no repeated values, the mode is ____________.
a) The highest value
b) Not calculable
c) The lowest value
ii. The mean of 25, 28, 25, 32, and 30 is ____________.
a) 28
b) 30
c) 29
iii. In a dataset: 6, 8, 12, 14, 18, 20, the median is ____________.
a) 12
b) 14
c) 18
iv. If a group of 12 has a mean of 15 and a second group of 18 has a mean of 20, the mean of the combined group of 30 can be found by calculating the ____________ of the values and dividing by the ____________ of the combined group.
a) Sum, total size
b) Average, total sum
c) Median, mean
i. In a dataset: 4, 5, 6, 7, 8, the mode is ____________.
a) 4
b) 5
c) None
ii. The mean of 22, 24, and 26 is ____________.
a) 24
b) 25
c) 26
iii. In a dataset: 9, 11, 13, 15, 17, the median is ____________.
a) 13
b) 15
c) 17
[mediator_tech]