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 5th - grade mean

Count the number of dots for each value and multiply by the value. Then sum these products and divide by the total number of dots.
For 5th - grade:
Number of dots: \(2 + 3+1 + 5+7 + 4+3+2+1=28\)
\((0\times2 + 1\times3+2\times1 + 3\times5+4\times7 + 5\times4+6\times3+7\times2+8\times1)\div28=(0 + 3+2 + 15+28 + 20+18+14+8)\div28 = 108\div28\approx3.86\)

Step2: Calculate 7th - grade mean

Count the number of dots for each value and multiply by the value. Then sum these products and divide by the total number of dots.
For 7th - grade:
Number of dots: \(1+2+3+5+6+4+3+2+1 = 27\)
\((0\times1+1\times2 + 2\times3+3\times5+4\times6+5\times4+6\times3+7\times2+8\times1)\div27=(0 + 2+6 + 15+24+20+18+14+8)\div27 = 107\div27\approx3.96\)

Step3: Calculate 5th - grade median

Arrange the data in ascending order. Since there are \(n = 28\) data - points (an even number), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th ordered values.
The 14th and 15th ordered values are both 4, so the median is 4.

Step4: Calculate 7th - grade median

Arrange the data in ascending order. Since there are \(n = 27\) data - points (an odd number), the median is the \(\frac{n + 1}{2}\)th ordered value.
\(\frac{27+1}{2}=14\)th ordered value. Counting the dots in ascending order, the 14th value is 4.

Answer:

The 5th - grade mean is approximately \(3.86\)
The 7th - grade mean is approximately \(3.96\)
The 5th - grade median is 4
The 7th - grade median is 4