Solution: 1. The mean is given below:
[tex]Mean=\frac{\sum fx}{\sum f}[/tex]
Where:
[tex]f[/tex] is the frequency
[tex]x[/tex] is the value
[tex]\therefore Mean=\frac{1 \times 7 + 2 \times 1+ 3 \times 3 + 4 \times 2 + 5\times 2}{15}[/tex]
[tex]=\frac{7+2+9+8+10}{15} =\frac{36}{15} =2.4[/tex]
Therefore, the mean = 2.4
2. The mean is given below:
[tex]Mean = \frac{8+11+23+15}{4}[/tex]
[tex]=\frac{57}{4}[/tex]
[tex]=14.3[/tex]
I am not understanding why your teacher 14.3 is wrong. Please check whether the weight of 4 pumpkins is correct or not.
3. We are given that on average 5 passengers will board the bus at each of the 6 stops.
Let x be the number of passengers board the bus at the sixth stop.
Therefore, the average is:
[tex]\frac{3+7+5+6+2+x}{6} =5[/tex]
[tex]23+x=30[/tex]
[tex]x=30-23[/tex]
[tex]x=7[/tex]
Therefore, 7 passengers need to board the bus at the sixth stop for Leah's prediction to be true.
