Question 1
100 adults are asked their weights, which were recorded in the following table:
Fill in the missing values for cumulative frequency.
Select the correct answer from the list below:
A:
B:
C:
D:
CORRECT ANSWER: C
WORKED SOLUTION:
Answer: C
For this question you need to add the previous cumulative frequency row to the the frequency of the row you are on.
Level 6
Question 2
The following table shows the number of goals scored by a football team over the course of 30 games. Find the median and mode number of goals scored.
Select the correct answer from the list below:
A: Mode = 4 and Median = 2
B: Mode = 10 and Median = 3
C: Mode = 3 and Median = 3
D: Mode = 3 and Median = 2
CORRECT ANSWER: D: Mode = 3 and Median = 2
WORKED SOLUTION:
To fine the mode we just need to look at which entry has the highest frequency, which is 3 goals.
There are 30 data points, so the median is \dfrac{30+1}{2}=15.5th term. Drawing the cumulative frequency will help figure out where this is.
Because the 15th and 16th entries are both 2, then so is the median.
Level 6
Question 2
Use the following frequency table to plot a cumulative frequency diagram for the weights of 100 adults
Select the correct answer from the list below:
A:
B:
C:
D:
CORRECT ANSWER: D
WORKED SOLUTION:
To plot a cumulative frequency diagram we take the end of the class interval as the x coordinate and its respective cumulative frequency as the y coordinate, e.g. (50,5), (60,25), (70,58), (80,84), (100,97), and (110,100).
And now we need to connect the dots with a smooth curve
Level 6
Question 3
Use the following frequency table to construct a cumulative frequency diagram for the time taken to run a race.
Select the correct answer from the list below:
A:
B:
C:
D:
CORRECT ANSWER: A
WORKED SOLUTION:
To plot a cumulative frequency diagram we take the end of the class interval as the x coordinate and its respective cumulative frequency as the y coordinate, e.g. (25,3), (30,10), (40,25), (45,40), (50,46), and (60,47).
And now we need to connect the dots with a smooth curve
Level 6
Question 4
Use the cumulative frequency diagram below to create a box plot for the amount of money spent on entertainment every month by 48 people.
Select the correct answer from the list below:
A:
B:
C:
D:
CORRECT ANSWER: C
WORKED SOLUTION:
To construct a box plot we need to know five things: smallest value, lower quartile, median, upper quartile, and the highest value.
Luckily, we can read off the lowest and highest values immediately, 0 and 80.
Then, because we have 48 people in the data set, we get:
Q_1=48\times\frac{1}{4}=12^{th}\textrm{ term}
Q_2=48\times\frac{1}{2}=24^{th}\textrm{ term}
Q_3=48\times\frac{3}{4}=36^{th}\textrm{ term}
So, now we know where the two quartiles and the median are, we can draw across from these values on the y-axis to find the corresponding amount of money spent on the x-axis. This looks like:
Reading along the x-axis we get Q_1=25, Q_2=38, and Q_3=48
Using this we get the following boxplot:
Level 6
Question 5
Use the cumulative frequency diagram below to create a box plot for the amount of times 56 people went to restaurants over the course of a month.
Select the correct answer from the list below:
A:
B:
C:
D:
CORRECT ANSWER: B
WORKED SOLUTION:
To construct a box plot we need to know five things: smallest value, lower quartile, median, upper quartile, and the highest value.
Luckily, we can read off the lowest and highest values immediately, 0 and 16.
Then, because we have 56 people in the data set, we get:
Q_1=56\times\frac{1}{4}=14^{th}\textrm{ term}
Q_2=56\times\frac{1}{2}=28^{th}\textrm{ term}
Q_3=56\times\frac{3}{4}=42^{th}\textrm{ term}
So, now we know where the two quartiles and the median are, we can draw across from these values on the y-axis to find the corresponding amount of times people visit restaurants the x-axis. This looks like:
Reading along the x-axis we get Q_1=3, Q_2=8, and Q_3=11
Using this we get the following boxplot:
Level 6