Math Problem Statement

Find the mean (average) from a set of weights of 30 students and calculate the mean from a frequency table showing student scores.

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).

Mean=weights30\text{Mean} = \frac{\sum \text{weights}}{30}

First, calculate the sum: 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=138440 + 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 = 1384

Now, divide by 30: Mean=138430=46.13kg\text{Mean} = \frac{1384}{30} = 46.13 \, \text{kg}

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)
602
653
704
755
803
854
905
954
1002

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:

(60×2)+(65×3)+(70×4)+(75×5)+(80×3)+(85×4)+(90×5)+(95×4)+(100×2)(60 \times 2) + (65 \times 3) + (70 \times 4) + (75 \times 5) + (80 \times 3) + (85 \times 4) + (90 \times 5) + (95 \times 4) + (100 \times 2)

=120+195+280+375+240+340+450+380+200=2580= 120 + 195 + 280 + 375 + 240 + 340 + 450 + 380 + 200 = 2580

Step 2: Sum of frequencies
The total number of students is the sum of the frequencies:

2+3+4+5+3+4+5+4+2=322 + 3 + 4 + 5 + 3 + 4 + 5 + 4 + 2 = 32

Step 3: Calculate the Mean
Now, divide the weighted sum by the total frequency to find the mean:

Mean=258032=80.625\text{Mean} = \frac{2580}{32} = 80.625

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:

  1. How do we interpret the mean in terms of weight distribution for the class?
  2. Why is it important to consider frequency when calculating the mean from a table?
  3. How does the frequency distribution affect the overall mean in problem 2?
  4. What other statistical measures could be used to analyze this data set?
  5. 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