Each of 60 students was asked to draw a 20° angle without using a protractor - Edexcel - A-Level Maths Statistics - Question 1 - 2015 - Paper 1
Question 1
Each of 60 students was asked to draw a 20° angle without using a protractor. The size of each angle drawn was measured. The results are summarised in the box plot b... show full transcript
Worked Solution & Example Answer:Each of 60 students was asked to draw a 20° angle without using a protractor - Edexcel - A-Level Maths Statistics - Question 1 - 2015 - Paper 1
Step 1
Find the range for these data.
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Answer
To find the range, we subtract the smallest value from the largest value recorded in the box plot. The minimum value is 9 and the maximum value is 48.
Thus, the range is:
Range=Max−Min=48−9=39
Step 2
Find the interquartile range for these data.
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Answer
The interquartile range (IQR) is calculated by subtracting the lower quartile (Q1) from the upper quartile (Q3). From the box plot, Q1 is at 12 and Q3 is at 25.
So, the IQR is:
IQR=Q3−Q1=25−12=13
Step 3
Use linear interpolation to estimate the size of the median angle drawn. Give your answer to 1 decimal place.
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To find the median, we need to locate the 30th and 31st values (since there are 60 students).
From the table:
The angle range 70 ≤ a < 75 has 11 students, which includes the 30th and 31st.
Thus, we find the median between 70 and 75.
We calculate:
Median=70+0.5(75−70)=70+2.5=72.5
Thus the estimated median is approximately 72.5°.
Step 4
Show that the lower quartile is 63°.
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Answer
To find the lower quartile, we find the first quartile, which is the 15th student in the ordered list of angles. From the table:
The ranges are as follows:
55 ≤ a < 60: 6 students
60 ≤ a < 65: 15 students
Adding the groups, the 15th student falls into the 60 ≤ a < 65 range. The lower quartile is therefore calculated to be around 63°.
Step 5
Show that there are no outliers for these data.
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To identify outliers, we compute the outlier limits using the lower and upper quartiles along with the IQR:
As all data points fall between -7.5 and 94.5, there are no outliers.
Step 6
Draw a box plot for these data on the grid on page 3.
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The box plot should represent the minimum (9), Q1 (12), median (63), Q3 (25), and maximum (48). Draw a box from Q1 to Q3 with a line at the median and whiskers extending to the minimum and maximum values.
Step 7
State which angle the students were more accurate at drawing. Give reasons for your answer.
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Answer
The median for the 70° angle is closer to the target (70°) than the median for the 20° angle (which is 72.5°). This indicates that the students were more accurate at drawing the 70° angle, as the deviation from the target angle is smaller.
