#### Related Questions VIEW ALL [62]

The following table givens the age of 50 student of a class . find the arithmetic mean of thier agges.

Age- Years |
16-18 |
18-20 |
20-22 |
22-24 |
24-26 |

No.of students |
2 | 7 | 21 | 17 | 3 |

Using step- deviation method , calculate the mean marks of the following distribution.

C.I | 50-55 | 55-60 | 60-65 | 65-70 | 70-75 | 75-80 | 80-85 | 85-90 |

Frequency | 5 | 20 | 10 | 10 | 9 | 6 | 12 | 8 |

From the following cumulative frequency table , find :

Median

Lower quartile

Upper quaetile

Marks (less than ) |
10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |

Cumulative frequency |
5 | 24 | 37 | 40 | 42 | 48 | 70 | 77 | 79 | 80 |

The age of 40 students are given in the following table :

Age (in yrs) | 12 | 13 | 14 | 15 | 16 | 17 | 18 |

Frequency | 2 | 4 | 6 | 9 | 8 | 7 | 4 |

The following distribution represents the height of 160 students of a school.

Height (in cm) |
No. of Students |

140 – 145 | 12 |

145 – 150 | 20 |

150 – 155 | 30 |

155 – 160 | 38 |

160 – 165 | 24 |

165 – 170 | 16 |

170 – 175 | 12 |

175 – 180 | 8 |

Draw an ogive for the given distribution taking 2 cm = 5 cm of height on one axis and 2 cm = 20 students on the other axis. Using the graph, determine:

(1) The median height.

(2) The interquartile range.

(3) The number of students whose height is above 172 cm.

Find mean by step- deviation method:

C.i | 63-70 | 70-77 | 77-84 | 84-91 | 91-98 | 98-105 | 105-112 |

Freq | 9 | 13 | 27 | 38 | 32 | 16 | 15 |

At a shooting competition the score of a competitor were as given below

Score | 0 | 1 | 2 | 3 | 4 | 5 |

No.of shots | 0 | 3 | 6 | 4 | 7 | 5 |

(1)What was his modal score?

(2) What was his median score?

(3) What was his total score ?

(4) What was his mean score?

The following table given the weekly of workers in a factory:

Weekly wages (in Rs) |
No.of workers |

50-55 | 5 |

55-60 | 20 |

60-65 | 10 |

65-70 | 10 |

70-75 | 9 |

75-80 | 6 |

80-85 | 12 |

85-90 | 8 |

Calcculate: (1)the mean, (2) the model class, (3) th number of workers getting weekly qages below Rs. 80 and (4) the number of workers getting Rs . 65 or more but less than Rs.85 as weekly wages.

The content of 100 match boxes were checked to detemine the number of matches they contained .

no of matches |
35 | 36 | 37 | 38 | 39 | 40 | 41 |

no of boxes |
6 | 10 | 18 | 25 | 21 | 12 | 8 |

(1) Calculate, correct to one decimal place, the means number of matches per box .

(2) Determine how many extra matches would have to be added to the the total contents of the total content of the 100 boxes to bring the mean up to exactly 39 matches.

The mean of the folowing is 62.8 and the sum of all the frequencies is 50. find the missing frequency `f_1 and f_2`

Class | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 | 100-120 |

Freq | 5 | `f_1` | 10 | `f_2` | 7 | 8 |

From the data given below . calculate the mean wage, correct to the nnearst rupee.

category |
A |
B |
C |
D |
E |
F |

Wages (Rs,day)(x) |
50 | 60 | 70 | 80 | 90 | 100 |

no.of workers |
2 | 4 | 8 | 12 | 10 | 6 |

(1) If the number of workers in each category is doubled, , what would be the new mean wage?

(2) If the wages per day in each category are incresed by 60% what is the new mean wages?

(3) If the number of workers in each caategory is doubled is and the wages per day worker are reduced by 40%, what would be the new mean wage?

In a malaria epidemic, the number of cases diagnosed were as follows:

Date july | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |

num | 5 | 12 | 20 | 27 | 46 | 30 | 31 | 18 | 11 | 5 | 0 | 1 |

on what days do the mode and upper and lower quartiles occur?

Calculate the mean of the following distribution :

Class Interval | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |

Frequency | 8 | 5 | 12 | 35 | 24 | 16 |

The following are the marks obtained by 70 boys in a class test:

Marks | No. of boys |

30-40 | 10 |

40-50 | 12 |

50-60 | 14 |

60-70 | 12 |

70-80 | 9 |

80-90 | 7 |

90-100 | 6 |

Calculate the mean by :

Short - cut method

The folloeing table shows the expenditure of 60 boys on books. find the mode of their expenditure:

Expenditure (Rs) | No.of students |

20-25 | 4 |

25-30 | 7 |

30-35 | 23 |

35-40 | 18 |

40-45 | 6 |

45-50 | 2 |

The following are the marks obtained by 70 boys in a class test:

Marks | No. of boys |

30-40 | 10 |

40-50 | 12 |

50-60 | 14 |

60-70 | 12 |

70-80 | 9 |

80-90 | 7 |

90-100 | 6 |

Calculate the mean by :

Step - deviation method

The following table gives the hights of plants in centimeter. If the mean height if plants is 60.95 cm; find the value of `f`.

Height (cm) | 50 | 55 | 58 | 60 | 65 | 70 | 71 |

no of plants | 2 | 4 | 10 | f | 5 | 4 | 3 |

Draw an ogive for the data given beelow and from the graph determine:

(1) the median marks

(2) the number of students who obtained more than 75% marks

Marks |
No.of students |

0-9 | 5 |

10-19 | 9 |

20-29 | 16 |

30-39 | 22 |

40-49 | 26 |

50-59 | 18 |

60-69 | 11 |

70-79 | 6 |

80-89 | 4 |

90-99 | 3 |

Find the mean of the following distribution by step deviation method:

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

Frequency | 10 | 6 | 8 | 12 | 5 | 9 |

Attempt this question on graph paper.

Age (yrs ) |
5-15 | 15-25 | 25-35 | 35-45 | 45-55 | 55-65 | 65-75 |

No.of casualties |
6 | 10 | 15 | 13 | 24 | 8 | 7 |

(1)Construct the 'less than' Cumulative frequency curve for the above data. using 2 cm =10 years on one axis and 2 cm =10 casualties on the other.

(2)From your graph determine :

(a)the median

(b)the lower quartile

By drawing an ogive, estimate the following frequency distribution:

Weight (kg) | 10-15 | 15-20 | 20-25 | 25-30 | 30-35 |

No.of boys | 11 | 25 | 12 | 5 | 2 |

Attempt this question on a graph paper. The table shows the distribution of marks gained by a group of 400 students in an examination.

Marks (Less than ) |
10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |

No.of student | 5 | 10 | 30 | 60 | 105 | 180 | 270 | 355 | 390 | 400 |

Using scaie of 2cm to represent 10 marks and 2 cm to represent 50 student, plot these point and draw a smooth curve though the point

Estimate from the graph :

(1)the midian marks

(2)the quartile marks

Marks obtained by 40 students in a short assessment is given below, where a and b are two missing data.

Marks | 5 | 6 | 7 | 8 | 9 |

Number of Students | 6 | a | 16 | 13 | b |

If the mean of the distribution is 7.2, find a and b.

The following table given the weekly wages of workers in a factory.

Weekly Wages |
No.of workers |

50-55 | 5 |

55-60 | 20 |

60-65 | 10 |

65-70 | 10 |

70-75 | 9 |

75-80 | 6 |

80-85 | 12 |

85-90 | 8 |

Calculate the mean by using:

Direct Method

If the mean of the following obseervations is 54, find the value of `p`

Class |
0-20 | 20-40 | 40-60 | 60-80 | 80-100 |

Frequency |
7 | p | 10 | 9 | 13 |

c

c

c Weekly wages (Rs) |
No.of workers |

50-55 | 5 |

55-60 | 20 |

60-65 | 10 |

65-70 | 10 |

70-75 | 9 |

75-80 | 6 |

80-85 | 12 |

85-90 | 8 |

Calculate the mean by ussing:

Short-Cut method

Using a graph paper draw a histogram of the given distribution showing the number of runs scored by 50 batsmen. Estimate the mode of the data:

Runs scored |
3000- 4000 |
4000- 5000 |
5000- 6000 |
6000- 7000 |
7000- 8000 |
8000- 9000 |
9000- 10000 |

No. of batsmen |
4 | 18 | 9 | 6 | 7 | 2 | 4 |

The distribution given below shows the marks obtained by 25 students in an aptitude test. Find the mean, median and mode of the distribution.

Marks obtained | 5 | 6 | 7 | 8 | 9 | 10 |

No. of students | 3 | 9 | 6 | 4 | 2 | 1 |

Find the mode of following data, using a histogram:

Class |
0-10 | 10-20 | 20-30 | 30-40 | 40-50 |

Frequency |
5 | 12 | 20 | 9 | 4 |

The Mean of the following distribution is 52 and the frequency of class interval 30-40 is ‘f’. Find ‘f’.

Class Interval |
10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |

Frequency | 5 | 3 | f | 7 | 2 | 6 | 13 |

Draw a histogram from the following frequency distribution and find the mode from the graph:

Class | 0-5 | 5-10 | 10-15 | 15-20 | 20-25 | 25-30 | |

Frequency | 2 | 5 | 18 | 14 | 8 | 5 |

If the mean of the following distribution is 24, find the value of 'a '.

Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |

Number of students |
7 | a | 8 | 10 | 5 |

The marks of 200 students in a test were recorded as follows:

Marks |
No. of students |

10-19 | 7 |

20-29 | 11 |

30-39 | 20 |

40-49 | 46 |

50-59 | 57 |

60-69 | 37 |

70-79 | 15 |

80-89 | 7 |

Construct the cumulative frequency table. Drew the ogive and use it too find:

(1) the median and

(2) the number of student who score more than 35% marks.

Find the mode and median of the following frequency distribution

x | 10 | 11 | 12 | 13 | 14 | 15 |

f | 1 | 4 | 7 | 5 | 9 | 3 |

The mean of the following distribution is `21 1/7 `. find the value of `f`

C.I | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |

Freq | 8 | 22 | 31 | f | 2 |

1) Using step–deviation method, calculate the mean marks of the following distribution.

2) State the modal class.

Class Interval | 50 - 55 | 55 - 60 | 60 - 65 | 65 - 70 | 70 - 75 | 75 - 80 | 80 - 85 | 85 – 90 |

Frequency | 5 | 20 | 10 | 10 | 9 | 6 | 12 | 8 |

In a school, 100 pupils have heights as tabulate below:

Height (in cm ) | No. of pupils |

121-130 | 12 |

131-40 | 16 |

141-150 | 30 |

151-160 | 20 |

161-170 | 14 |

171-180 | 8 |

Find the median height by drawing an ogive.

The following table shows the frequency distribution of heights of 51 boys:

Height (cm) |
120 | 121 | 122 | 123 | 124 |

Frequency |
5 | 8 | 18 | 10 | 9 |

find the mode of heights.

Calculate the mean of the distribution given below using the shortcut method.

Marks | 11-20 | 21-30 | 31-40 | 41-50 | 51-60 | 61-70 | 71-80 |

No. of students | 2 | 6 | 10 | 12 | 9 | 7 | 4 |

Calculate the mean of the following distribution using step deviation method.

Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |

Number of students |
10 | 9 | 25 | 0 | 16 | 10 |