Statistics — Class 10 Mathematics (Standard) PYQs

While calculating mean of a grouped frequency distribution, step deviation method was used $\left(\frac{x-a}{h}=u\right)$. It was found that $\bar{x}=64$, $h = 5$ and $a = 62.5$. The value of $\bar{u}$ is

(a) Find the mean and mode of the following frequency distribution :
| Class Interval | 400-450 | 450-500 | 500-550 | 550-600 | 600-650 | 650-700 |
| Frequency | 15 | 18 | 20 | 23 | 22 | 12 |
OR
(b) If the median of the following frequency distribution is $32.5$ and sum of all frequencies is $40$, then find the values of $f_1$ and $f_2$ :
| Class Interval | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |
| Frequency | 3 | $f_1$ | 9 | 12 | 6 | $f_2$ | 2 |

(a) The mean of the following distribution is $53$. Find the missing frequency $p$.
| Class Interval | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 |
| Frequency | 12 | 15 | $p$ | 28 | 13 |
Hence, find mode of the distribution.
OR
(b) Compute median of the following data :
| Mid-value | 115 | 125 | 135 | 145 | 155 | 165 | 175 |
| Frequency | 12 | 15 | 20 | 16 | 10 | 16 | 11 |

Mode and Mean of a data are $15x$ and $18x$, respectively. Then the median of the data is :

Find the missing frequency $f$ in the following table, if the mean of the given data is $18$. Hence find the mode.
| Daily Allowance | 11-13 | 13-15 | 15-17 | 17-19 | 19-21 | 21-23 | 23-25 |
| Number of Children | 7 | 6 | 9 | 13 | $f$ | 5 | 4 |

The following frequency distribution gives the monthly consumption of electricity of $68$ consumers of a locality. Find the mean and mode of the data :
| Monthly Consumption (in units) | 65-85 | 85-105 | 105-125 | 125-145 | 145-165 | 165-185 | 185-205 |
| Number of Consumers | 4 | 5 | 13 | 20 | 14 | 8 | 4 |

What is the mode of a data if median and mean of the same data are $9.6$ and $10.5$, respectively ?

The lengths of $40$ leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table :
| Length (in mm) | 118-126 | 127-135 | 136-144 | 145-153 | 154-162 | 163-171 | 172-180 |
| Number of Leaves | 3 | 5 | 9 | 12 | 5 | 4 | 2 |
Find the median length of the leaves.

Find the Mean and Mode of the following frequency distribution :
| Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |
| Frequency | 8 | 7 | 15 | 20 | 12 | 8 | 10 |

Find the mean and median for the following data :
| Classes | 5-15 | 15-25 | 25-35 | 35-45 | 45-55 | 55-65 | 65-75 |
| Frequency | 2 | 3 | 5 | 7 | 4 | 2 | 2 |