Question

nadya put the data she collected during her survey in a table. then she found the mean of each of the four rows of data.
population data
2 4 5 4 5
2 4 2 4 3
4 3 2 4 4
3 4 4 3 2
find the mean from each row of data. between what values will the mean of the actual population be found?
3.2 and 3.4
3.2 and 4
3.4 and 4
3 and 4

Explanation:

Step1: Calculate mean of first row

The first - row data is 2, 4, 5, 4, 5. The mean formula is $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n = 5$ and $\sum_{i=1}^{5}x_{i}=2 + 4+5 + 4+5=20$. So the mean $\bar{x}_1=\frac{20}{5}=4$.

Step2: Calculate mean of second row

The second - row data is 2, 4, 2, 4, 3. Here $n = 5$ and $\sum_{i = 1}^{5}x_{i}=2 + 4+2 + 4+3 = 15$. So the mean $\bar{x}_2=\frac{15}{5}=3$.

Step3: Calculate mean of third row

The third - row data is 4, 3, 2, 4, 4. Here $n = 5$ and $\sum_{i = 1}^{5}x_{i}=4 + 3+2 + 4+4 = 17$. So the mean $\bar{x}_3=\frac{17}{5}=3.4$.

Step4: Calculate mean of fourth row

The fourth - row data is 3, 4, 4, 3, 2. Here $n = 5$ and $\sum_{i = 1}^{5}x_{i}=3 + 4+4 + 3+2 = 16$. So the mean $\bar{x}_4=\frac{16}{5}=3.2$.

Step5: Determine range of population mean

The means of the rows are 4, 3, 3.4, 3.2. The minimum of these means is 3.2 and the maximum is 4. So the mean of the actual population will be between 3.2 and 4.

Answer:

3.2 and 4