Photo AI
The table gives information about the weekly wages of 80 people - Edexcel - GCSE Maths - Question 13 - 2020 - Paper 1
Question 13
The table gives information about the weekly wages of 80 people. Wage (£w) Frequency 200 < w ≤ 250 5 250 < w ≤ 300 10 300 < w ≤ 350 20 350 < w ≤ 400 ... show full transcript
Worked Solution & Example Answer:The table gives information about the weekly wages of 80 people - Edexcel - GCSE Maths - Question 13 - 2020 - Paper 1
Step 1
Complete the cumulative frequency table:
Answer
To complete the cumulative frequency table, we need to calculate the cumulative frequency for each wage band. This is done by adding the frequency of the current band to the cumulative frequency of the previous band:
- For 200 < w ≤ 250: Cumulative Frequency = 5
- For 250 < w ≤ 300: Cumulative Frequency = 5 (previous) + 10 = 15
- For 300 < w ≤ 350: Cumulative Frequency = 15 (previous) + 20 = 35
- For 350 < w ≤ 400: Cumulative Frequency = 35 (previous) + 15 = 50
- For 400 < w ≤ 450: Cumulative Frequency = 50 (previous) + 5 = 55
- For 450 < w ≤ 500: Cumulative Frequency = 55 (previous) + 15 = 70
Step 2
Draw a cumulative frequency graph for your completed table:
Answer
To draw the cumulative frequency graph:
- Mark the wage ranges on the x-axis (200 to 500 pounds).
- Mark the corresponding cumulative frequencies on the y-axis (up to 80).
- Plot the points based on the completed table:
- (250, 5)
- (300, 15)
- (350, 35)
- (400, 50)
- (450, 55)
- (500, 70)
- Connect these points with a smooth curve.
Step 3
Juan says "60% of this group of people have a weekly wage of £360 or less."
Answer
To find out if Juan is correct, we need to determine the cumulative frequency for wages of £360 or less.
-
From the table, we have:
- For £350: Cumulative Frequency = 35
- For £400: Cumulative Frequency = 50 (not applicable since we want £360 or less)
-
The cumulative frequency for £350 is 35. To find the percentage, we calculate:
ext{Percentage} = rac{35}{80} imes 100 = 43.75\
ext{Percentage} ightarrow 43.75\
Thus, since 43.75% is less than 60%, Juan is incorrect.