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ICSE Class 10 Mathematics Question 21 of 21

Solved 2023 Question Paper ICSE Class 10 Mathematics — Question 20

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20
Question

Question 10(ii)

Use graph paper to answer this question.

During a medical checkup of 60 students in a school, weights were recorded as follows :

Weight (in kg)Number of students
28-302
30-324
32-3410
34-3613
36-3815
38-409
40-425
42-442

Taking 2 cm = 2 kg along one axis and 2 cm = 10 students along the other axis draw an ogive. Use your graph to find the :

(a) median

(b) upper quartile

(c) number of students whose weight is above 37 kg.

Answer

(a)

Weight (in kg)Number of students (f)Cumulative frequencies (c.f.)
28-3022
30-3246
32-341016
34-361329
36-381544
38-40953
40-42558
42-44260
TotalΣf = 60

Here, n = 60, which is even.

Median = n2\dfrac{n}{2} th term = 602\dfrac{60}{2} = 30th term.

Steps of construction :

  1. Take 1 cm = 2 kg on x-axis.

  2. Take 1 cm = 10 students on y-axis.

  3. Since, x axis starts at 28 hence, a kink is drawn at the starting of x-axis. Plot the point (28, 0) as ogive starts on x-axis representing lower limit of first class.

  4. Plot the points (30, 2), (32, 6), (34, 16), (36, 29), (38, 44), (40, 53), (42, 58) and (44, 60).

  5. Join the points by a free-hand curve.

  6. Draw a line parallel to x-axis from point A (no. of students) = 30, touching the graph at point B. From point B draw a line parallel to y-axis touching x-axis at point C.

Use graph paper to answer this question. ICSE 2023 Maths Solved Question Paper.

From graph, C = 36.2

Hence, median = 36.2 kg

(ii) Here, n = 60, which is even.

By formula,

Upper quartile = 3n4=3×604\dfrac{3n}{4} = \dfrac{3 \times 60}{4} = 45th term.

Draw a line parallel to x-axis from point D (no. of students) = 45, touching the graph at point E. From point E draw a line parallel to y-axis touching x-axis at point F.

From graph, F = 38.2 kg

Hence, upper quartile = 38.2 kg.

(iii) Draw a line parallel to y-axis from point G (weight) = 37 kg, touching the graph at point H. From point H draw a line parallel to x-axis touching y-axis at point I.

From graph, I = 38.

∴ 38 students have weight less than or equal to 37 kg.

No. of students whose weight is more than 37 kg = 60 - 38 = 22.

Hence, no. of students whose weight is more than 37 kg = 22.