# NCERT Class 10 Chapter 14 Statistics CBSE Board Sample Problems Long Answer

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## Question

**The lengths of 50 leaves of a plant are measured correct to the nearest millimeter and the data obtained is represented in the following table**

Length (in mm) | 109-117 | 118-126 | 127-135 | 136-144 | 145-153 | 154-162 | 163-171 |

No. of leaves | 4 | 6 | 14 | 13 | 6 | 4 | 3 |

Find the mean length of the leaves.

### Solution

Class Interval | ||||

108.5-117.5 117.5-126.5 126.5-135.5 135.5-144.5 144.5-153.5 153.5-162.5 162.5-171.5 | 113 122 131 140 149 158 167 | 4 6 14 13 6 4 3 | -3 -2 -1 0 1 2 3 | -12 -12 -14 0 6 8 9 |

Total |

Given frequency distribution is not continuous. So first we have to make it continuous.

Here assumed mean (a) =140; class size =9

Now,

Hence, mean length of the leaves -137.30mm.

## Question

**Draw a ‘less than type’ ogive for the following frequency distribution.**

Class | 15-20 | 20-25 | 25-30 | 30-35 | 35-40 | 40-45 |

Frequency | 13 | 18 | 31 | 25 | 15 | 5 |

### Solution

Class | Frequency |

Less than 20 Less than 25 Less than 30 Less than 35 Less than 40 Less than 45 | 13 |

## Question

**In a retail market, fruit vendor were selling mangoes in packing boxes. These boxes contained varying number or mangoes. The following was the distribution.**

No. of mangoes | 50-52 | 53-55 | 56-58 | 59-61 | 62-64 |

No. of boxes | 15 | 110 | 135 | 115 | 25 |

Find the mean and median number of mangoes kept in a packing box.

### Solution

Class interval | Mid value () | (where a=57) | |||

49.5-52.5 52.5-55.5 55.5-58.5 58.5-61.5 61.5-64.5 | 51 54 57=a 60 63 | -2 -1 0 1 2 | 15 110 135 115 25 | -30 -110 0 115 50 | 15 125 260 375 400 |

Mean

For median: Median

Here

Median class is 55.5-58.5

Median

## Question

**The following table gives production yield of rice per hectare in some farms of a village:**

Production yield (in kg/hectare) | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |

No. of farms | 3 | 9 | 12 | 20 | 6 |

Draw a more than type’ ogive. Also, find median from the curve.

### Solution

Production yield (in kg/hectare) Class interval | Frequency | Production yield more than or eual to | |

10-20 20-30 30-40 40-50 50-60 | 3 9 12 20 6 | 10 20 30 40 50 | 50 47 38 26 6 |

## Question

Life time (in hours) | More than or equal to 240 | More than or equal to 280 | More than or equal to 320 | More than or equal to 360 | More than or equal to 400 | More than or equal to 440 | More than or equal to 480 |

Number of bulbs | 100 | 95 | 87 | 77 | 47 | 22 | 10 |

**Draw a more than type ogive and from it find median. Verify it by actual calculations.**

### Solution

More than or equal to | Number of bulbs |

240 280 320 360 400 440 480 | 100 95 87 77 47 22 10 |

Median from curve is 396.

Class interval | Frequency | Cumulative frequency | |

240-280 280-320 320-360
400-440 440-480 480-520 | 5 8 10
25 12 10 | 5 13 23
78 90 100 | Median class |

100 |

Median

## Question

**Change the following distribution to a ‘more than type’ distribution. Hence draw the ‘more than type’ ogive for this distribution.**

Class Interval | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 |

Frequency | 10 | 8 | 12 | 24 | 6 | 25 | 15 |

### Solution

Class Interval | Cumulative Frequency |

More than or equal to 20 | 100 |

More than or equal to 30 | 90 |

More than or equal to 40 | 82 |

More than or equal to 50 | 70 |

More than or equal to 60 | 46 |

More than or equal to 70 | 40 |

More than or equal to 80 | 15 |

Plot of points (20. 100), (30. 90), (40, 82), (50. 70), (60,46), (70. 40) and (80. 15)

Join the points to get a curve

## Question

**The mean of the following distribution is 18. Find the frequency f of the class 19 —21.**

Class | 11-13 | 13-15 | 15-17 | 17-19 | 19-21 | 21-23 | 23-25 |

Frequency | 3 | 6 | 9 | 13 | f | 5 | 4 |

### Solution

Class | x | f | |

11-13 | 12 | 3 | 36 |

13-15 | 14 | 6 | 84 |

15-17 | 16 | 9 | 144 |

17-19 | 18 | 13 | 234 |

19-21 | 20 | f | 20f |

21-23 | 22 | 5 | 110 |

23-25 | 24 | 4 | 96 |

Mean

## Question

**If the median of the following frequency distribution is 32.5. Find the values of** **and** **.**

Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 70-80 | Total |

Frequency | 5 | 9 | 12 | 3 | 2 | 40 |

### Solution

Class | Frequency | Cumulative Frequency |

0-10 | ||

10-20 | 5 | |

20-30 | 9 | |

30-40 | 12 | |

40-50 | ||

50-60 | 3 | |

60-70 | 2 | |

40 |

Median median class is 30-40.

Now

Also,

## Question

**The following distribution gives the daily income of 50 workers of a factory**

Daily Income | 400-420 | 400-420 | 400-420 | 400-420 | 400-420 |

Number of workers | 12 | 12 | 12 | 12 | 12 |

Convert this distribution to less than a type of cumulative frequency distribution and draw its ogive.

### Solution

Daily Income | Number of workers | Cumulative Frequency |

400-420 | 12 | 12 |

420-440 | 14 | 26 |

440-460 | 8 | 34 |

460-480 | 6 | 40 |

480-500 | 10 | 50 |

Correct Table

Drawing an ogive with coordinates

## Question

**Calculate Mean of the following distribution**

C.I | 10-19 | 20-29 | 30-39 | 40-49 | 50-59 | 60-69 | 70-79 | 80-89 | 90-99 |

Frequency | 5 | 9 | 13 | 17 | 16 | 11 | 12 | 9 | 8 |

### Solution

10-19 | 14.5 | 5 | -40 | -4 | 20 |

20-29 | 24.5 | 9 | -30 | -3 | -27 |

30-39 | 34.5 | 13 | -20 | -2 | -26 |

50-50 | 44.5 | 17 | -10 | -1 | -17 |

40-49 | 54.5 | 16 | 0 | 0 | 0 |

60-69 | 64.5 | 11 | 10 | 1 | 11 |

70-79 | 74.5 | 12 | 20 | 2 | 24 |

80-89 | 84.5 | 9 | 30 | 3 | 27 |

90-99 | 94.5 | 8 | 40 | 4 | 32 |

100 |

## Question

**If the mean of x and** **is M, find the mean of** **and**

### Solution

Mean of and is