Histograms

Question 1

How do you find the frequencies from a histogram?

Answer 1

Calculate the area of each bar (base x height)

Question 2

What type of data does a histogram represent?

Answer 2

Continuous Data

e.g. Time, Length, Mass etc.

Question 3

What is name for the scale on the y-axis of a histogram?

Answer 3

Frequency Density

Question 4

What is the difference between a Bar Chart and a Histogram?

Answer 4

For a Histogram:

It does not have gaps between the bars.

The area of each bar is the frequency (not the height).

It is used for continuous data (not discrete data)

Question 5

Using the ‘area of a square’ method;
How do you complete the histogram and frequency table?

Answer 5

Find a bar that has the frequency given.
Split it into equal squares.
Calculate what each square represents.
Produce a key.

Divide the other bars into squares to find their frequencies.
(fill the table in)

Use the frequencies from the table to produce the missing bars.
Fill them evenly from the bottom.

Question 6

How do you produce a histogram from a frequency table?

Answer 6

Work out the ‘Base’ from each ‘Class Width’.

Work out the ‘Frequency Density’ or ‘Height’ of each bar.
‘Frequency’ divided by ‘class width’ (area/base)

Fill in the scale for the ‘Frequency Density’ on the y-axis.

Draw the bars on the grid.

Question 7

How do you complete the histogram and frequency table?

Answer 7

Work out the ‘Base’ from each ‘Class Width’.

Find a bar that has the frequency given.
Use this to calculate the ‘Height’ of the bar.

Use the ‘Height’ of the bar to produce the scale for the ‘Frequency Density’ on the y-axis.

Calculate the other frequencies from the bars given.
(Base x height)
Fill the frequency table in.

Calculate the ‘Height’ of the missing bars.
‘Frequency’ divided by ‘class width’ (Area/Base)
Draw the bars on the grid.

Question 8

From the histogram, how would you find the number of trains that were between 15 and 35 minutes late?

Answer 8

Draw a line up from 15 minutes to create a new bar.

Draw a line up from 35 minutes to create a new bar.

Calculate the area of the bars between the two values to find the frequencies.

Add these frequencies together.

Question 9

From the histogram, how would you find the Median?

Answer 9

Add the frequencies together and divide by 2 to find the middle position.

Calculate the area (frequency) of the first bars untill you reach just before the middle position.

A bar needs to be created that will give the remainder of the needed frequencies.

The width of this last bar is found by dividing the needed frequency by the height.

Draw a line at this point to read the median value.