# NCERT Class 10 Chapter 14 Statistics CBSE Board Sample Problems Long Answer (For CBSE, ICSE, IAS, NET, NRA 2022)

Doorsteptutor material for CBSE/Class-10 is prepared by world's top subject experts: get questions, notes, tests, video lectures and more- for all subjects of CBSE/Class-10.

## 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 - 117.5117.5 - 126.5126.5 - 135.5135.5 - 144.5144.5 - 153.5153.5 - 162.5162.5 - 171.5 113122131140149158167 461413643 -3-2-10123 -12-12-140689 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 20Less than 25Less than 30Less than 35Less than 40Less 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 - 52.552.5 - 55.555.5 - 58.558.5 - 61.561.5 - 64.5 515457 = a6063 -2-1012 1511013511525 -30-110011550 15125260375400

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 - 2020 - 3030 - 4040 - 5050 - 60 3912206 1020304050 504738266

## 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 240280320360400440480 100958777472210

Median from curve is 396.

 Class interval Frequency Cumulative frequency 240 - 280280 - 320320 - 360360 - 400400 - 440440 - 480480 - 520 581030251210 51323537890100 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

Mean of and is

Developed by: