Question

(b) the grouped frequency table shows the length to the nearest minute of some phone calls that a doctor made.
time (minutes) frequency
7 to 12 7
13 to 18 5
19 to 24 8
25 to 30 4
31 to 36 1
(i) how many calls lasted between 13 and 18 minutes?
(ii) how many phone calls lasted 24 minutes or less?
(iii) what is the total number of phone calls made?
(iv) what fraction of the calls lasted 25 or more minutes?
(d) the grouped frequency table shows the amount spent in a supermarket by its customers.
amount spent (£) frequency
0 < a ≤ 20 24
20 < a ≤ 40 15
40 < a ≤ 60 8
60 < a ≤ 80 10
80 < a ≤ 100 3
(i) how many customers were surveyed?
(ii) how many customers spent more than £60?
(iii) what percentage of customers spent between £20 and £40?
(iv) tao says “20 people spent between £50 and £70”. is tao correct?

Explanation:

Step1: Find calls between 13 - 18 minutes

Check the frequency for 13 - 18 minutes in the phone - call table.
The frequency is 5.

Step2: Find calls 24 minutes or less

Sum frequencies of 7 - 12, 13 - 18, 19 - 24 minutes in the phone - call table.
$7 + 5+8=20$

Step3: Find total phone calls

Sum all frequencies in the phone - call table.
$7 + 5+8 + 4+1=25$

Step4: Find fraction of calls 25 or more minutes

Sum frequencies of 25 - 30 and 31 - 36 minutes in the phone - call table: $4 + 1=5$. Then find the fraction with respect to the total number of calls.
The fraction is $\frac{5}{25}=\frac{1}{5}$

Step5: Find number of surveyed customers

Sum all frequencies in the supermarket table.
$24+15 + 8+10+3=60$

Step6: Find customers who spent more than £60

Sum frequencies of 60 < A ≤ 80 and 80 < A ≤ 100 in the supermarket table.
$10 + 3=13$

Step7: Find percentage of customers who spent between £20 and £40

Use the formula $\text{Percentage}=\frac{\text{Frequency}}{\text{Total frequency}}\times100\%$.
The frequency of customers who spent between £20 and £40 is 15, and the total frequency is 60. So the percentage is $\frac{15}{60}\times100\% = 25\%$

Step8: Check Tao's statement

The grouped frequency table has intervals 40 < A ≤ 60 and 60 < A ≤ 80. There is no way to know exactly how many customers spent between £50 and £70 from the given grouped data. So Tao is incorrect.

Answer:

(i) 5
(ii) 20
(iii) 25
(iv) $\frac{1}{5}$
(d)(i) 60
(d)(ii) 13
(d)(iii) 25%
(d)(iv) No