CBSE 2025 · Region 5 · Set 2 · Q32 · 5 marks
During a medical checkup, height of $\displaystyle 35$ students of a class were recorded as follows: Height (in cm) $\displaystyle 90$-$\displaystyle 100$ $\displaystyle 100$-$\displaystyle 110$ $\displaystyle 110$-$\displaystyle 120$ $\displaystyle 120$-$\displaystyle 130$ $\displaystyle 130$-$\displaystyle 140$ $\displaystyle 140$-$\displaystyle 150$ Number of Students $\displaystyle 3$ $\displaystyle 2$ $\displaystyle 4$ $\displaystyle 5$ $\displaystyle 14$ $\displaystyle 7$
Find the difference between the mean height and median height.
| Height (in cm) | $\displaystyle 90$-$\displaystyle 100$ | $\displaystyle 100$-$\displaystyle 110$ | $\displaystyle 110$-$\displaystyle 120$ | $\displaystyle 120$-$\displaystyle 130$ | $\displaystyle 130$-$\displaystyle 140$ | $\displaystyle 140$-$\displaystyle 150$ |
| Number of Students | $\displaystyle 3$ | $\displaystyle 2$ | $\displaystyle 4$ | $\displaystyle 5$ | $\displaystyle 14$ | $\displaystyle 7$ |
Marking-scheme solution
| Height (in cm) | Number of Students \(\displaystyle \left(f_{\mathrm{i}}\right)\) | \(\displaystyle x_{\mathrm{i}}\) | \(\displaystyle u_{\mathrm{i}=\frac{x_{i}-115}{10}}^{10}\) | \(\displaystyle f_{\mathrm{i}} u_{\mathrm{i}}\) | \(\displaystyle c f\) |
| $\displaystyle 90$-$\displaystyle 100$ | $\displaystyle 3$ | $\displaystyle 95$ | -$\displaystyle 2$ | -$\displaystyle 6$ | $\displaystyle 3$ |
| $\displaystyle 100$-$\displaystyle 110$ | $\displaystyle 2$ | $\displaystyle 105$ | -$\displaystyle 1$ | -$\displaystyle 2$ | $\displaystyle 5$ |
| $\displaystyle 110$-$\displaystyle 120$ | $\displaystyle 4$ | $\displaystyle 115$ = a | $\displaystyle 0$ | $\displaystyle 0$ | $\displaystyle 9$ |
| $\displaystyle 120$-$\displaystyle 130$ | $\displaystyle 5$ | $\displaystyle 125$ | $\displaystyle 1$ | $\displaystyle 5$ | $\displaystyle 14$ |
| $\displaystyle 130$-$\displaystyle 140$ | $\displaystyle 14$ | $\displaystyle 135$ | $\displaystyle 2$ | $\displaystyle 28$ | $\displaystyle 28$ |
| $\displaystyle 140$-$\displaystyle 150$ | $\displaystyle 7$ | $\displaystyle 145$ | $\displaystyle 3$ | $\displaystyle 21$ | $\displaystyle 35$ |
| Total | $\displaystyle 35$ | $\displaystyle 46$ |
StatisticsMean of Grouped DataApplylong_answermedium
More from Statistics
- 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 x median + y mean = z mode; is the empirical relationship between mean, median and mode, then the value of…2025 · asked 3×
- Following data shows the marks obtained by 100 students in a class test: The median will be the average of…2025 · asked 3×
- The India Meteorological Department observes seasonal and annual rainfall every year in different…2025 · asked 3×
- If the maximum number of students has obtained 52 marks out of 80, then2025 · asked 3×
- The cumulative frequency for calculating median is obtained by adding the frequencies of all the:2025 · asked 3×
- If the mean of 2,9, x+6,2 x+3,5,10,5 is 7, then the value of x is:2025 · asked 2×
- Mode and Mean of a data are 15x and 18x, respectively. Then the median of the data is:2025 · asked 2×
CBSE Class 10 Mathematics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.