Question

I need help filling out the blanks in the picture

Answer 1

We have a table that classify 20 vehicles in terms of their speed in certain sector.

a) We have to find how many drivers drove 35 miles per hour or less.

To do that we can add the number of drivers for speeds of 35 or less.

We can do this as:

`\begin{gathered} n_(35)+n_(34)+n_(33)+n_(29) \\ 5+4+2+1 \\ 12 \end{gathered}`

Then, we know that 12 drivers drove at 35 miles per hour or less.

b) We now have to find how many drivers drove at more than 35 miles per hour.

As we already calculate the number of drivers at 35 miles per hour or less and we know that the total number of drivers is 20, then we can calculate this as:

`n_(>35)=N-n_(\le35)=20-12=8`

NOTE: We could also have count for the categories over 35: 3+2+2+1 = 8

c) We can find the average speed as:

`\begin{gathered} \bar{v}=(1)/(N)\sum ^8_(k\mathop=1)v_kx_k=(1)/(20)(29\cdot1+33\cdot2+34\cdot4+35\cdot5+36\cdot3+38\cdot2+39\cdot2+54\cdot1) \\ \bar{v}=(1)/(20)(29+66+136+175+108+76+78+54) \\ \bar{v}=(1)/(20)(722) \\ \bar{v}=36.1 \end{gathered}`

The average speed is 36.1 milesper hour.

d) The median speed is the speed for which half of the drivers are below this speed and the other half above that speed.

Then, as we have 20 drivers, the median will be the average between the 10th and 11th driver speed.

If we look at the table, we see that 7 drivers drove at 34 miles per hour or less.

If we move one category up, 12 drivers drove at 35 miles per hour or less.

Then, both the 10th and 11th drivers both were driving at 35 miles per hour. Then, the average between their speed is also 35 miles per hour.

Then, the median is 35 miles per hour.

e) The mode is the value of the category with the most absolute frequency.

In this case, is also 35 miles per hour, which has a frequency of 5 drivers.

Answer:

a) There are 12 drivers that drove at 35 miles per hour or less.

b) There are 8 drivers that drove at more than 35 miles per hour.

c) The average speed is 36.1 miles per hour.

d) The median is 35 miles per hour.

e) The mode is 35 miles per hour.