Photo AI
The box plot shows information about the sales, in thousands of pounds (£000s), of an online store each month - Edexcel - GCSE Maths - Question 11 - 2022 - Paper 2
Question 11
The box plot shows information about the sales, in thousands of pounds (£000s), of an online store each month. Andrew says, "Three quarters of the given data lies ... show full transcript
Worked Solution & Example Answer:The box plot shows information about the sales, in thousands of pounds (£000s), of an online store each month - Edexcel - GCSE Maths - Question 11 - 2022 - Paper 2
Step 1
Explain why Andrew is wrong.
Answer
Andrew is incorrect because he states that three quarters of the data lies between the lower quartile and the upper quartile. In statistics, the lower quartile (Q1) and the upper quartile (Q3) define the interquartile range (IQR), which contains the middle 50% of the data, not three quarters. Specifically, Q1 is the 25th percentile, and Q3 is the 75th percentile of the dataset. Hence, only 50% of the data is between these two quartiles.
Step 2
Draw a box plot for the shop sales.
Answer
To draw the box plot:
- Mark the least value (30) on the grid.
- Mark the lower quartile (80) on the grid.
- Mark the median (170) on the grid.
- Mark the upper quartile (260) on the grid.
- Mark the greatest value (350) on the grid.
- Connect the points to form the box from 80 to 260 (the IQR), with a line at the median (170), and lines (whiskers) extending from 30 to 80 and from 260 to 350.
Step 3
Compare the distribution of the sales of the online store with the distribution of the sales in the shop.
Answer
When comparing the online store and the shop, the distributions can be analyzed through their respective box plots. For the online store, the interquartile range, median, and overall spread can be observed. If the online store's IQR is wider than that of the shop, it indicates more variability in sales. Additionally, the median of the online sales can be compared to that of the shop to assess central tendency. The online store may also show a different range of sales compared to the shop, which may indicate differing consumer behavior or seasonal effects in sales patterns.