Activities like running or cycling reduce stress and the risk of mental disorders like depression. Running helps build…
CBSE Class 10 Maths PYQ · Statistics · Find Mean, median, mode · 4 Marks · March 2024 · Standard
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404 Marks · March 2024 · Standard
Activities like running or cycling reduce stress and the risk of mental disorders like depression. Running helps build endurance. Children develop stronger bones and muscles and are less prone to gain weight. The physical education teacher of a school has decided to conduct an inter school running tournament in his school premises. The time taken by a group of students to run $100 \text{ m}$, was noted as follows : Based on the above, answer the following questions : (i) What is the median class of the above given data ? (ii) (a) Find the mean time taken by the students to finish the race. OR (b) Find the mode of the above given data. (iii) How many students took time less than $60$ seconds ?
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Time (in seconds) | Number of students $0-20$ | $8$ $20-40$ | $10$ $40-60$ | $13$ $60-80$ | $6$ $80-100$ | $3$ Total | $40$ (i) Correct Cummulative Frequency Median class = $40-60$ (ii) (a) Correct table for $x_i$ and $f_ix_i$ Time (in sec) | Number of students (f) | $x_i$ | cf | $f_ix_i$ $0-20$ | $8$ | $10$ | $8$ | $80$ $20-40$ | $10$ | $30$ | $18$ | $300$ $40-60$ | $13$ | $50$ | $31$ | $650$ $60-80$ | $6$ | $70$ | $37$ | $420$ $80-100$ | $3$ | $90$ | $40$ | $270$ Total | $40$ | | | $1720$ Mean = $$\begin{aligned}& \frac{1720}{40} = 43 \\ & \text{OR} \\ & (b) \text{ Modal class } = 40-60 \\ & \text{Mode } = 40 + \frac{(13-10)}{(26-10-6)} \times 20 \\ & = 46 \\ & (iii)\end{aligned}$$31 students took time less than 60 seconds$
