Math Problem Statement
Solution
Let's break down and solve the two tasks shown in the image.
1. Finding the Mean Weight from the Data:
The problem asks to determine the average (mean) weight from the data set given for 30 students.
Step 1: List of Weights
The data set contains the following weights (in kg):
40, 45, 50, 45, 91, 43,
42, 50, 52, 47, 43, 52,
45, 49, 50, 46, 48, 47,
49, 48, 47, 46, 47, 50,
49, 47, 43, 49, 43, 45.
Step 2: Calculate the Mean To calculate the mean, sum all the weights and then divide by the total number of students (30).
First, calculate the sum:
Now, divide by 30:
So, the mean weight is approximately 46.13 kg.
2. Finding the Mean from the Frequency Table:
The table provides the scores and their frequencies for a class, and we need to calculate the mean score.
Score (Nilai Siswa) | Frequency (Frekuensi) |
---|---|
60 | 2 |
65 | 3 |
70 | 4 |
75 | 5 |
80 | 3 |
85 | 4 |
90 | 5 |
95 | 4 |
100 | 2 |
Step 1: Calculate the sum of products of scores and their frequencies
To calculate the weighted sum of the scores, multiply each score by its frequency:
Step 2: Sum of frequencies
The total number of students is the sum of the frequencies:
Step 3: Calculate the Mean
Now, divide the weighted sum by the total frequency to find the mean:
Thus, the mean score is approximately 80.63.
Would you like further clarification or details on any part of the solution? Here are some follow-up questions related to this task:
- How do we interpret the mean in terms of weight distribution for the class?
- Why is it important to consider frequency when calculating the mean from a table?
- How does the frequency distribution affect the overall mean in problem 2?
- What other statistical measures could be used to analyze this data set?
- Can you describe the significance of outliers in a data set like the one in problem 1?
Tip: When working with large data sets, organizing data systematically (like using frequency tables) helps make calculations much easier!
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Math Problem Analysis
Mathematical Concepts
Mean Calculation
Frequency Table
Averages
Formulas
Mean = (Sum of all values) / (Number of values)
Weighted Mean = (Sum of (score * frequency)) / (Total frequency)
Theorems
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Suitable Grade Level
Grade 8