✓ Board-verified↻ asked 2×
Mathematics · 2023 · 5 marks
CBSE 2023 · Region 2 · Set 1 · Q34
A student noted the number of cars passing through a spot on a road for $\displaystyle 100$ periods each of $\displaystyle 3$ minutes and summarised it in the table given below. Find the mean and median of the following data. Number of cars $\displaystyle 0$-$\displaystyle 10$ $\displaystyle 10$-$\displaystyle 20$ $\displaystyle 20$-$\displaystyle 30$ $\displaystyle 30$-$\displaystyle 40$ $\displaystyle 40$-$\displaystyle 50$ $\displaystyle 50$-$\displaystyle 60$ $\displaystyle 60$-$\displaystyle 70$ $\displaystyle 70$-$\displaystyle 80$ Frequency (periods) $\displaystyle 7$ $\displaystyle 14$ $\displaystyle 13$ $\displaystyle 12$ $\displaystyle 20$ $\displaystyle 11$ $\displaystyle 15$ $\displaystyle 8$
| Number of cars | $\displaystyle 0$-$\displaystyle 10$ | $\displaystyle 10$-$\displaystyle 20$ | $\displaystyle 20$-$\displaystyle 30$ | $\displaystyle 30$-$\displaystyle 40$ | $\displaystyle 40$-$\displaystyle 50$ | $\displaystyle 50$-$\displaystyle 60$ | $\displaystyle 60$-$\displaystyle 70$ | $\displaystyle 70$-$\displaystyle 80$ |
| Frequency (periods) | $\displaystyle 7$ | $\displaystyle 14$ | $\displaystyle 13$ | $\displaystyle 12$ | $\displaystyle 20$ | $\displaystyle 11$ | $\displaystyle 15$ | $\displaystyle 8$ |
Marking-scheme solution
| Number of cars | \(\displaystyle \mathrm{x}_{\mathrm{i}}\) | \(\displaystyle \mathrm{f}_{\mathrm{i}}\) | \(\displaystyle \mathrm{x}_{\mathrm{i}} \mathrm{f}_{\mathrm{i}}\) | c.f. |
| $\displaystyle 0$-$\displaystyle 10$ | $\displaystyle 5$ | $\displaystyle 7$ | $\displaystyle 35$ | $\displaystyle 7$ |
| $\displaystyle 10$-$\displaystyle 20$ | $\displaystyle 15$ | $\displaystyle 14$ | $\displaystyle 210$ | $\displaystyle 21$ |
| $\displaystyle 20$-$\displaystyle 30$ | $\displaystyle 25$ | $\displaystyle 13$ | $\displaystyle 325$ | $\displaystyle 34$ |
| $\displaystyle 30$-$\displaystyle 40$ | $\displaystyle 35$ | $\displaystyle 12$ | $\displaystyle 420$ | $\displaystyle 46$ |
| $\displaystyle 40$-$\displaystyle 50$ | $\displaystyle 45$ | $\displaystyle 20$ | $\displaystyle 900$ | $\displaystyle 66$ |
| $\displaystyle 50$-$\displaystyle 60$ | $\displaystyle 55$ | $\displaystyle 11$ | $\displaystyle 605$ | $\displaystyle 77$ |
| $\displaystyle 60$-$\displaystyle 70$ | $\displaystyle 65$ | $\displaystyle 15$ | $\displaystyle 975$ | $\displaystyle 92$ |
| $\displaystyle 70$-$\displaystyle 80$ | $\displaystyle 75$ | $\displaystyle 8$ | $\displaystyle 600$ | $\displaystyle 100$ |
| Total | $\displaystyle 100$ | $\displaystyle 4070$ |
More from Statistics
- The dimensions of a window are 156 cm × 216 cm. Arjun wants to put grill on the window creating complete…2026 · asked 3×
- India meteorological department observes seasonal and annual rainfall every year in different sub-divisions…2023 · asked 3×
- If the mode of some observations is 10 and sum of mean and median is 25, then the mean and median…2025 · asked 3×
- If the mean and mode of a data are 12 and 21 respectively, then its median is:2026 · asked 3×
- If the value of each observation of a statistical data is increased by 3, then the mean of the data2023 · asked 3×
- The middle most observation of every data arranged in order is called:2024 · asked 3×
- If value of each observation in a data is increased by 2, then median of the new data2024 · asked 3×
- If x median + y mean = z mode; is the empirical relationship between mean, median and mode, then the value of…2025 · asked 3×
CBSE Class 10 Mathematics past-paper question from the 2023board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.