M17/5/MATSD/SP1/ENG/TZ2XX 6. For a study, a researcher collected leaves the leav
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Question
M17/5/MATSD/SP1/ENG/TZ2XX 6. For a study, a researcher collected leaves the leaves, in racted 200 leaves from oak trees. After measuring the lengths of in cm, she produced the following cumulative frequency graph. 200 180 60 HHEEE 140 120 100 80 60 40 20 5 6 7 89 10 11 12 length of leaf (cm) (a) Write down the median length of these leaves. (b) Write down the number of leaves with a length less than or equal to 8cm The researcher finds that 10% of the leaves have a length greater than k cm. (c) (0) Use the graph to find the value of k. Before measuring, the researcher estimated k to be approximately 9.5cm. Find the percentage error in her estimate. (il) 14] question continues on the following page)Explanation / Answer
1. After looking at the cumulative frequency graph.
Maximum height = 200. Since it is even.
N/2 , N/2 + 1
200÷ 2 = 100 , 100 +1 = 101
Corresponding to frequency 100 draw a horizontal line where it touches the graph.
Length of the leaves corresponding to this point is 9 cm.
And in correspondence to 101, it is approximately 9 again.
Hence median length of the leaves is 9 cm.
2. From the graph the nunber of leaves with length less than or equal to 8 is 40.
3. 10% of 200 is 20.
The length which corresponds to 180 will give us the value of k i.e 10.6 cm.
b) Error : (10.6 - 9.5)= 1.1
% error : (1.1/ 10.6) * 100 = 10.38%
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