Reading histograms

The Maths Habit Handout to print

  1. The class 0 < t ≤ 20 has a frequency of 14. Work out the frequency density.

    0.7
  2. The classes 20 < m ≤ 30 and 30 < m ≤ 60 both have a frequency of 15. Which bar is taller?

    20 < m ≤ 30
  3. The class 1.5 < h ≤ 2 has a frequency of 7. Work out the frequency density.

    14

A rectangle has an area of 24 squares.

What could its width and its height be?

1 and 24, 2 and 12, 3 and 8, 4 and 6, 1.5 and 16, …

frequency
= frequency density × class width
frequency = area of the bar

Estimate how many values are between 15 and 30.

(a) frequency for 10 < t ≤ 15 15

(b) estimate between 5 and 15 20

ClassClass widthFrequency densityFrequency
10 < t ≤ 155315
5 < t ≤ 10515

(a) frequency for 155 < h ≤ 175 20

(b) estimate between 150 and 165 25

ClassClass widthFrequency densityFrequency
155 < h ≤ 17520120
150 < h ≤ 1555315
155 < h ≤ 16510110

(a) frequency for 10 < t ≤ 15 15

(b) estimate between 5 and 15 20

ClassClass widthFrequency densityFrequency
10 < t ≤ 155315
5 < t ≤ 10515

(a) frequency for 30 < m ≤ 40 15

(b) estimate between 10 and 30 25

ClassClass widthFrequency densityFrequency
30 < m ≤ 40101.515
10 < m ≤ 20100.55
20 < m ≤ 3010220

Histograms worksheet, page 2

Answer sheet

  1. The bar for 10 < x ≤ 30 has a frequency of 40. The bar for 30 < x ≤ 35 is the same height. What is its frequency?

    10
  2. The bar for 0 < t ≤ 20 has a frequency density of 1.5. Estimate how many values are less than 8. What have you assumed?

    12. The values are spread evenly

  1. Find the frequency for 10 < t ≤ 25.

    24
    00.81.62.43.2Frequency density01020304050Time, t (minutes)
  2. Estimate how many values are between 20 and 30 minutes.

    22
  3. What have you assumed in question 2?

    The values are spread evenly in each class
Exit tickets to print