Question

the dot plot shows the number of hours, to the nearest hour, that a sample of 5th graders and 7th graders spend watching television each week. what are the mean and median? the 5th - grade mean is. the 7th - grade mean is. the 5th - grade median is. the 7th - grade median is

Explanation:

Step1: Calculate the 5th - grade mean

Count the number of dots (frequency) for each hour value.
For 5th grade:
Number of data points \(n_1=2 + 2+1 + 3+4 + 4+3 + 2+1=22\)
Sum of data \(S_1=(1\times2)+(2\times2)+(3\times1)+(4\times3)+(5\times4)+(6\times4)+(7\times3)+(8\times2)+(9\times1)\)
\(S_1 = 2+4 + 3+12+20+24+21+16+9=111\)
Mean \(\bar{x}_1=\frac{S_1}{n_1}=\frac{111}{22}\approx5\)

Step2: Calculate the 7th - grade mean

Count the number of dots (frequency) for each hour value.
For 7th grade:
Number of data points \(n_2 = 2+2+2+3+4+4+3+2+1=23\)
Sum of data \(S_2=(1\times2)+(2\times2)+(3\times2)+(4\times3)+(5\times4)+(6\times4)+(7\times3)+(8\times2)+(9\times1)\)
\(S_2=2 + 4+6+12+20+24+21+16+9 = 114\)
Mean \(\bar{x}_2=\frac{S_2}{n_2}=\frac{114}{23}\approx5\)

Step3: Calculate the 5th - grade median

Since \(n_1 = 22\) (even), the median is the average of the \(\frac{n_1}{2}=11\)th and \((\frac{n_1}{2}+1)=12\)th ordered data points.
Order the data:
After counting the cumulative frequencies:
The 11th and 12th data points are both 6. Median \(M_1 = 6\)

Step4: Calculate the 7th - grade median

Since \(n_2=23\) (odd), the median is the \(\frac{n_2 + 1}{2}=12\)th ordered data point.
Order the data:
After counting the cumulative frequencies, the 12th data point is 4. Median \(M_2=4\)

Answer:

The 5th - grade mean is \(5\), the 7th - grade mean is \(5\), the 5th - grade median is \(6\), the 7th - grade median is \(4\)