80 warm-up
TRANSCRIPT
IB Math Studies Yr 1
Name_________________________________
Date: ____________
WARM-UP: The graph below shows the cumulative frequency for the yearly incomes of 200 people.
Use the graph to estimate
(a) the number of people who earn less than 5000 British pounds per year;
(b) the median salary of the group of 200 people;
**(c) the interquartile range of the group of 200 people;
200
180
160
140
120
100
80
60
40
20
00 5000 10 000 15 000 20 000 25 000 30 000 35 000
Annual income in British pounds
Cumulativefrequency
Lesson 2-11: Practice with Cumulative Frequency
Learning Goals:
#1: What is cumulative frequency and how do we interpret cumulative frequency tables? #2: How do we interpret Cumulative Frequency Graphs?
IB Math Studies Yr 1
RECALL: HOW TO INTERPRET A CUMULATIVE FREQUENCY GRAPH
A cumulative frequency graph is a line graph that shows the cumulative frequencies.
In other words, a cumulative frequency graph shows the total frequencies that are less than the given x-value.
The last cumulative frequency on your graph should be the same as the grand total for the data distribution.
Example: The following cumulative frequency graph shows the times, to the nearest minute, taken by 100 students
to complete a mathematics task.
(a) Use your graph to estimate
i. the number of students that completed the task in less than 20 minutes.
ii. the number of students that completed the task in 20 minutes or more.
iii. the percentage of students that completed the task in 20 minutes or more
IB Math Studies Yr 1 Let’s try one together: A botanist has measured the heights of seedlings and has presented her findings on the
cumulative frequency graph below.
(a) How many seedlings have heights of 6 cm or less?
(b) What percentage of seedlings are taller than 8 cm?
(c) What is the interquartile range?
IB Math Studies Yr 1 Now You Try: The cumulative frequency graph below shows the examination scores of 80 students.
From the graph find
(a) the median value;
(b) the interquartile range;
(c) the 60th
percentile;
(d) the percentage of students who scored 50 or above on this examination.
80
70
60
50
40
30
20
10
10 20 30 40 50 60scores
cumulativefrequency
0
IB Math Studies Yr 1
Name_____________________________
Date _____________________________
Lesson 2-11: Homework
1. A random sample of 167 people who own mobile phones was used to collect data on the amount of time they
spent per day using their phones. The results are displayed in the table below.
Time spent per
day (t minutes) 0 t 15 15 t 30 30 t 45 45 t 60 60 t 75 75 t 90
Number of people 21 32 35 41 27 11
(a) State an estimate of the mean of the given table.
(b) Complete the following cumulative frequency table.
Time spent per
day (t minutes) t 15 t 30 t 45 t 60 t 75 t 90
Number of people 21
2. The table below shows the number and weight (w) of fish delivered to a local fish market one morning.
weight (kg) frequency cumulative frequency
0.50 ≤ w < 0.70 16 16
0.70 ≤ w < 0.90 37 53
0.90 ≤ w < 1.10 44 c
1.10 ≤ w < 1.30 d 120
1.30 ≤ w < 1.50 10 130
(a) Write down the value of c.
(b) Write down the value of d.
(c) In which class is the median?
IB Math Studies Yr 1
3. The cumulative frequency graph shows the speed, s, in kmh−1, of 120 vehicles passing a hospital gate.
a. Find the median speed of the vehicles.
b. Write down the 75th percentile.
c. Calculate the interquartile range.
d. The speed limit past the hospital gate is 50 kmh−1
Find the number of these vehicles that exceed the speed limit.
IB Math Studies Yr 1 4. The mean of the ten numbers listed below is 5.5.
4, 3, a, 8, 7, 3, 9, 5, 8, 3
(a) Find the value of a.
(b) Find the median of these numbers.
5. The following table shows the age distribution of teachers who actively play sports at Harrison High School.
Ages Number of players
20 ≤ x < 30 5
30 ≤ x < 40 4
40 ≤ x < 50 3
50 ≤ x < 60 2
60 ≤ x < 70 3
(a) Calculate an estimate of the standard deviation.
(b) On the following grid, construct a histogram to represent this data.