Students were asked how many hours during the weekend they studied for a Monday exam. Each row of the table represents one sample from the class. Find the mean of each sample.
| 11 | 8 | 9 | 4 |
|---|---|---|---|
| 6 | 6 | 2 | 6 |
| 14 | 0 | 3 | 7 |
| 5 | 4 | 5 | 2 |
Mean of samples in row 1: $\square$
Mean of samples in row 2: $\square$
Mean of samples in row 3: $\square$
Mean of samples in row 4: $\square
Answer (2)
Calculate the mean of row 1: 4 11 + 8 + 9 + 4 = 8
Calculate the mean of row 2: 4 6 + 6 + 2 + 6 = 5
Calculate the mean of row 3: 4 14 + 0 + 3 + 7 = 6
Calculate the mean of row 4: 4 5 + 4 + 5 + 2 = 4
The means of the samples in each row are 8 , 5 , 6 , 4 .
Explanation
Understanding the Problem We are given a table showing the hours spent studying by students, with each row representing a sample. Our goal is to find the mean (average) of each sample.
Calculating the Mean of Row 1 To find the mean of the first sample (row 1), we add the hours and divide by the number of values, which is 4. The hours are 11, 8, 9, and 4. So, the mean is calculated as: 4 11 + 8 + 9 + 4 = 4 32 = 8
Calculating the Mean of Row 2 To find the mean of the second sample (row 2), we add the hours and divide by 4. The hours are 6, 6, 2, and 6. So, the mean is calculated as: 4 6 + 6 + 2 + 6 = 4 20 = 5
Calculating the Mean of Row 3 To find the mean of the third sample (row 3), we add the hours and divide by 4. The hours are 14, 0, 3, and 7. So, the mean is calculated as: 4 14 + 0 + 3 + 7 = 4 24 = 6
Calculating the Mean of Row 4 To find the mean of the fourth sample (row 4), we add the hours and divide by 4. The hours are 5, 4, 5, and 2. So, the mean is calculated as: 4 5 + 4 + 5 + 2 = 4 16 = 4
Final Answer The means of the samples in each row are 8, 5, 6, and 4, respectively.
Examples
Understanding how to calculate the mean of a sample is useful in many real-life situations. For example, if you want to know the average test score of a group of students, you would calculate the mean of their scores. Similarly, if you want to find the average rainfall in a month, you would calculate the mean of the daily rainfall amounts. Calculating means helps us understand central tendencies in data, which is a fundamental concept in statistics and data analysis.
The means of the samples in each row are calculated as follows: Row 1: 8, Row 2: 5, Row 3: 6, and Row 4: 4. Each mean is found by adding the values in a row and dividing by the number of values. The final means are 8 , 5 , 6 , 4 .
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